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Standing next to the leader of South Korea at the White House on Friday, President Biden said he was “deeply concerned” about the nuclear threat from North Korea and said he wouldn’t repeat the mistakes of past administrations.Stefani Reynolds for The New York Times

President Biden said he was “deeply concerned” about the ongoing nuclear threat from North Korea and appointed a new envoy to open diplomatic channels to the country as he met with the leader of South Korea at the White House on Friday.

Standing next to President Moon Jae-in of South Korea at the end of a full day of meetings, Mr. Biden pledged to avoid what he said were the mistakes of past administrations, but offered few details about what he called a new coordination with allies in the region.

“We closely studied what others have tried, and what worked and what hasn’t worked. And, you know, we’re under no illusions how difficult this is. None whatsoever,” Mr. Biden said from the State Dining Room. “The past four administrations have not achieved the objective. It’s an incredibly difficult objective.”

Mr. Biden also announced that the United States would fully vaccinate 550,000 South Korean troops who interact closely with American soldiers, and said that the two countries would cooperate more closely to speed up production of coronavirus vaccines for the world’s poorer nations.

During the meeting, the two leaders also announced a series of South Korean investments in the United States in semiconductors and batteries for electric cars — ways of deepening a technological alliance amid heightened competition with China.

Mr. Moon, the second world leader to visit the White House during Mr. Biden’s presidency, has called denuclearization of the Korean Peninsula a “matter of survival” for his country and said one goal for his meeting with Mr. Biden was bringing North Korea “back on the path of dialogue.”

Mr. Biden — who has said he would require preconditions before meeting with Kim Jong-un, the leader of North Korea — said the new envoy, Sung Kim, a career diplomat, would begin that outreach, but did not provide specifics on Friday.

“I would meet with him if there was a commitment on which we met,” the president said. “And the commitment has to be that there’s discussion about his nuclear arsenal.”

North Korea’s arsenal of nuclear weapons and its stockpile of fuel have roughly doubled in the past four years, a steady rise that proceeded even as President Donald J. Trump held high-drama meetings with Mr. Kim. Experts say the North’s stockpile of nuclear arms is fast approaching the size of those of India, Pakistan and Israel — relatively small members of the club who are believed to have a hundred or so weapons, whereas the big players have thousands.

Privately, officials in the Biden administration admit they harbor no illusions that North Korea will ever give up the entirety of its program. Yet, like his predecessors, Mr. Biden has decided not to officially acknowledge the North as a nuclear state, aides say.

Any official acknowledgment that the North Korean arsenal is here to stay would revive long-simmering debates about whether U.S. allies like South Korea and Japan can depend on the American nuclear umbrella, which is essentially a security net for countries that do not have nuclear weapons of their own.

Robert J. Einhorn, a former State Department official who was long a nuclear expert for the agency, said a formal acknowledgment that North Korea is a nuclear state would “increase interest by South Korea and Japan in acquiring their own nuclear weapons.”

For months now, the Biden administration has been engaged in a North Korean strategy review, often in consultation with South Korea and Japan. But it has offered little detail in public about its conclusions, other than to avoid trying the grand bargain with Mr. Kim that Mr. Trump did. Instead of trying to wrap a peace treaty formally ending the Korean War, the promise of a new relationship between Pyongyang and Washington, and a sweeping disarmament plan into one package, it will turn back to small, confidence-building steps.

Mr. Moon was crucial in arranging the summit meetings between Mr. Trump and Mr. Kim and has continued to encourage dialogue between Washington and Pyongyang.

Turbine towers at an offshore wind farm near Gochang, South Korea. 
Jung Yeon-Je/Agence France-Presse — Getty Images

The United States is calling on South Korea to set more ambitious climate targets, an issue that will be a part of discussions when President Moon Jae-in meets with President Biden on Friday at the White House.

Last month John Kerry, Mr. Biden’s international climate envoy, traveled to South Korea and, according to officials in both countries, surprised members of Mr. Moon’s government by suggesting the country take “corresponding efforts” to the United States in reducing planet-warming emissions. That would nearly double South Korea’s current target of cutting carbon 24.4 percent below 2017 levels by the end of the decade.

South Korea, the world’s seventh-largest emitter of planet-warming carbon dioxide, is important to the Biden administration’s effort to show that other industrialized countries are acting vigorously against climate change.

“South Korea is one of the major countries that can say, ‘Look, together with America we are doing this’ so Biden doesn’t stand on the podium alone,” said Chung Min Lee, a senior fellow at the Carnegie Endowment for International Peace.

Officials in Seoul have made the environment a central pillar in the economic recovery from the pandemic, starting a multibillion dollar program to invest in electric vehicles, battery storage, smart grids and offshore wind farms. The country also has pledged to get to net-zero emissions by 2050 and to end funding of overseas coal plants.

At the same time, South Korea has seven coal plants under construction, according to the Global Energy Monitor, a San Francisco-based group that follows fossil fuel projects. And a new study by the Korea Advanced Institute of Science and Technology found that unless the government enacted aggressive new policies, the country would “fall embarrassingly short” in meeting its current targets.

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President Biden awarded Col. Ralph Puckett Jr., a 93-year-old Korean War hero, the Medal of Honor on Friday. The ceremony was done in conjunction with a visit by the president of South Korea.Stefani Reynolds for The New York Times

President Biden awarded a Korean War hero, Ralph Puckett Jr., the Medal of Honor on Friday, seven decades after he led 51 Rangers in fighting off successive waves of enemy counterattacks after he was gravely wounded by a hand grenade.

Colonel Puckett, 94, initially received a Distinguished Service Cross for his command of the Eighth U.S. Army Ranger Company in November 1950. But that citation was upgraded after a campaign by a retired Army officer who believed the actions by the young lieutenant from Georgia warranted the nation’s highest military honor.

“I wish our son Beau were able to see this,” Mr. Biden said as he placed the ribbon around Colonel Puckett’s neck, invoking the memory of his late son, Beau Biden, who served in the Army Judge Advocate General’s Corps.

Mr. Biden honored Colonel Puckett, who has also been decorated for his valor in Vietnam, during a visit to the White House by President Moon Jae-in of South Korea. It was the first time Mr. Biden has issued the medal as president — and the first time a foreign leader was present for such a ceremony, according to White House officials.

The Korean War, a bloody and inconclusive stalemate often referred to as a “forgotten” war because it was fought in the shadows of World War II and Vietnam, claimed the lives of 36,574 American soldiers, along with millions of Korean and Chinese soldiers and civilians.

First Lt. Puckett, his rank at the time, was hit in the foot by a hand grenade as he began to organize the defense of an American-controlled hill against a chaotic assault by a Chinese force that greatly outnumbered his own.

But he refused medical evaluation, and darted in and out of his foxhole to rally his men, exposing himself repeatedly to danger as a decoy to locate the source of enemy fire, according to an oral history project documenting his heroism.

“Puckett risked his life by running across the area to draw fire that would reveal the location of the nest,” Mr. Biden recounted. “It took three runs intentionally exposing himself to the enemy to pick off the gunner.”

When the Chinese finally overran the position, Lieutenant Puckett — who had been hit by mortar fire twice after his foot was nearly blown off — ordered his company to evacuate and said he wanted to be left behind.

Two Rangers ignored him, and carried him behind the lines to safety.

He would recover, and go on to serve in Vietnam, before retiring as a colonel in 1971 as one of the most decorated combat veterans in the country’s history.

During his 22-year career, he received the Distinguished Service Cross twice, as well as two Silver Stars for valor, two Bronze Star Medals and five Purple Hearts.

Colonel Puckett would go on to serve as an executive with Outward Bound, a nonprofit educational organization that exposes students, especially those from cities, to wilderness settings.

Traffic flowing through a construction area near the Bay Bridge in Annapolis, Md., on Friday.
Jim Watson/Agence France-Presse — Getty Images

The Biden administration sent Senate Republicans an offer for a bipartisan infrastructure agreement on Friday that sliced more than $500 billion off the president’s initial proposal, a move that administration officials hoped would jump-start the talks but that Republicans greeted with disappointment.

The sides remain far apart. Mr. Biden’s latest offer is for $1.7 trillion in spending. Republicans have offered a $588 billion proposal, though many Democrats consider that offer even smaller, because it includes extensions of some federal infrastructure spending at expected levels. In a memo to Republicans on Friday, obtained by The New York Times, administration officials assessed the Republican offer as no more than $225 billion “above current levels Congress has traditionally funded.”

Mr. Biden’s new offer makes no effort to resolve the even thornier problem dividing the parties: how to pay for that spending. Mr. Biden wants to raise taxes on corporations, which Republicans oppose. Republicans want to repurpose money from Mr. Biden’s $1.9 trillion economic aid package, signed in March, and to raise user fees like the gas tax, which Mr. Biden opposes.

Still, the new proposal represents some movement from the White House. It cuts out a major provision of Mr. Biden’s American Jobs Plan: hundreds of billions of dollars for advanced manufacturing and research and development efforts meant to position the country to compete with China for dominance in emerging industries like advanced batteries. Lawmakers have included some, but not all, of the administration’s proposals in those areas in a bipartisan bill working its way through the Senate.

Mr. Biden’s counteroffer also reduces the amount of money he wants to spend on broadband internet and on highways and other road projects. He would essentially accept the Republicans’ offer of $65 billion for broadband, down from $100 billion, and reduce his highway spending plans by $40 billion to meet them partway. And his offer would create a so-called infrastructure bank to use public seed capital to leverage private infrastructure investment, which Republicans have pushed for.

Republican senators were still reviewing the offer Friday afternoon and planned to meet with White House officials again next week. But one Republican familiar with the talks said senators were disappointed that the offer did not move more significantly from the president’s earlier position and dismissed many of the changes as accounting shifts or updates to reflect spending already being debated on the Senate floor.

Democratic leaders on Capitol Hill have watched the talks skeptically, wary that Republicans will eat up valuable time on the legislative calendar and ultimately refuse to agree to a deal large enough to satisfy liberals. While they have given the White House and Republican senators latitude to pursue an alternative, party leaders are under increasing pressure from progressives to move a bill unilaterally through the arcane budget reconciliation process in the Senate.

They have quietly taken steps to make that possible in case the talks collapse. Aides to Senator Chuck Schumer, Democrat of New York and the majority leader, and Senator Bernie Sanders of Vermont, the chairman of the Budget Committee, met on Thursday with the Senate parliamentarian to discuss options for proceeding without Republicans.

Administration officials were frustrated that Republicans did not move more toward the president in an offer they presented in negotiations on Capitol Hill earlier this week. They made clear to Republicans on Friday that they expected to see significant movement in the next counteroffer, and that the timeline for negotiations was growing short, a person familiar with the discussions said.

White House officials have said publicly that they see Memorial Day as a deadline of sorts for determining whether a bipartisan deal might be possible.

Gaza residents surveying the damage to their homes on Friday.
Hosam Salem for The New York Times

The United States plans to be at the forefront of an international effort to help rebuild Gaza, an undertaking that is likely to cost billions of dollars and include restoring health and education services and other reconstruction, a senior Biden administration official said on Thursday.

The official said that rebuilding Gaza — likely to be coordinated through the United Nations — was at the top of a list of diplomatic considerations in the region now that a cease-fire between Israel and Palestinian militants was underway.

The administration is also considering how to foster relations and coordination among Palestinian political factions in Gaza and the West Bank. The rivalry between the Palestinian Authority, which exerts partial control in parts of the occupied territories, and Hamas, which governs Gaza and which the United States, Israel and others consider a terrorist group, has been a major obstacle in international efforts to aid Palestinians.

Rebuilding Gaza is a necessary part of the diplomacy — not only to help residents, but also because officials and experts said it could help create leverage with Hamas, which has lost popularity among residents who criticize its authoritarian approach and poor administration.

But Dennis B. Ross, a veteran American negotiator of peace efforts between Israel and the Palestinians, said that international donors would be wary of financing a costly reconstruction effort without assurances that any investments would not go to waste — as they all but certainly would if Hamas reignited hostilities.

Similar warnings were posed in 2014 after an eight-week war between Israel and Hamas damaged more than 170,000 homes in Gaza, displacing over a quarter of its population. The international community created a monitoring system to oversee the rebuilding efforts and block any attempts by Hamas to import supplies that could be used as weapons.

Mr. Ross said that any future monitoring system would need to be an effective, round-the-clock endeavor that would halt reconstruction if Hamas were found to be storing, building or preparing to launch rockets.

“The issue is massive reconstruction for no rockets,” Mr. Ross said. “There has to be enough oversight of this process to know that it’s working the way it’s intended. And the minute you see irregularities, everything stops.”

President Biden chose quiet diplomacy rather than public pressure on Israel to end the violence.
Doug Mills/The New York Times

As violence raged between Israeli and Hamas for 10 days, President Biden spoke with Benjamin Netanyahu, the Israeli prime minister, privately six times, conversations in which he pressed him to answer a simple question: “How does this end?”

Mr. Biden’s tactic was to avoid public condemnation of Israel’s bombing of Gaza — or even a public call for a cease-fire — in order to build up capital with Mr. Netanyahu and then exert pressure in private when the time came, according to two people familiar with the administration’s internal debates.

In private conversations, Mr. Biden and other American officials reiterated to the Israelis that they had achieved some significant military objectives against Hamas, the militant group that fired thousands of rockets at Israel from Gaza, including targeting its tunnel networks. Mr. Biden pressed Mr. Netanyahu on what his objective was, and what would allow him to say he had achieved it so that a shorter war was possible, rather than a drawn-out military conflict.

In response, according to the people familiar with the discussions, Mr. Netanyahu did not lay out specific objectives that he had to accomplish before agreeing to a cease-fire.

At the same time, Richard N. Haass, president of the Council on Foreign Relations, cautioned against exaggerating how much credit Mr. Biden deserved for setting the stage for a truce.

“About 90 percent of the reason for the cease-fire is that both Hamas and the government of Israel determined that prolonging the conflict didn’t serve their interests,” Mr. Haass said. “This was a cease-fire that essentially was ready to happen.”

In his public comments, Mr. Biden refused to join the growing calls from world leaders and many of his fellow Democrats for a cease-fire, or express anything short of support for Israel’s right to defend itself.

Dennis B. Ross, who has served as Middle East envoy to three presidents, said a public demand for a cease-fire could have backfired. Had Mr. Biden called for a cease-fire, Mr. Ross said, “Bibi’s political need to stand up to him would have been much greater.”

Mr. Biden’s approach, he added, also sent a message to Hamas. “The more they understood we were not going to be pressuring Israel that way, the more they understood they can’t count on us stopping Israel,” he said.

Mr. Biden’s strategy of quiet diplomacy was intended to build credibility with the Israelis, in order to privately push them toward an end to the violence in a final conversation with Mr. Netanyahu on Wednesday. And it took into account the need to tread carefully with Mr. Netanyahu.

Aware of the mistakes made by the United States in trying to mediate the 2014 Israel-Gaza conflict, Mr. Biden and his team did not want the United States to become the focus of the story. Instead, Mr. Biden tried to create space for Mr. Netanyahu, whom he will need as a partner in the future in dealing with Iran, to achieve his objectives.

“Israel and the United States are going to have big things to work out, in particular Iran,” Mr. Haas said. “The president had to be careful in how he handled Bibi. Both needed to maintain a working relationship so that if and when the Iran situation moved to the front burner, they would be able to work together.”

Mr. Biden began his conversations with Mr. Netanyahu by making no demands. That helped to pave the way for a gently worded statement that came after their third phone call, in which Mr. Biden said he would support a cease-fire, but stopped short of demanding one.

In follow up conversations on Tuesday and Wednesday, Mr. Biden built up the pressure by demanding privately to Mr. Netanyahu the need for a cease-fire.

State Senator Anthony Bouchard of Wyoming at a rally in Cheyenne in January. 
Michael Ciaglo/Getty Images

A Wyoming state senator who is challenging Representative Liz Cheney in the 2022 Republican primary acknowledged this week that when he was 18, he had sex with a 14-year-old girl — which is statutory rape in many states — and that she became pregnant.

The state senator, Anthony Bouchard, made the disclosure in a Facebook Live video posted on Thursday and in a subsequent interview with The Casper Star-Tribune, saying that the girl gave birth to a son “more than 40 years ago” in Florida and that he married the girl after she turned 15.

She died by suicide a few years later, after they had divorced and she had entered another relationship, Mr. Bouchard said.

Mr. Bouchard sought to downplay his actions, saying in his video, “She was a little younger than me, so it’s like the Romeo and Juliet story.” But under current Florida law, his actions would be illegal.

Because he did not specify the year he impregnated the girl, it is not clear what Florida’s laws were at the time.

Mr. Bouchard said he went public with the story after a newspaper reached out to him. In the Star-Tribune interview, he blamed a “political opposition research company” for spreading it.

He used his video to highlight his stance against abortion, saying he and the girl had resisted pressure to terminate the pregnancy.

There was “a lot of pressure, pressure to abort a baby, I got to tell you,” he said in the 13-minute video. “I wasn’t going to do it, and neither was she. And there was pressure to have her banished from their family. Just pressure. Pressure to go hide somewhere. And the only thing I could see as the right thing to do was to get married and take care of him.”

Mr. Bouchard is one of several Republicans who have said they will challenge Ms. Cheney, who was kicked out of her House leadership position this month for criticizing former President Donald J. Trump and saying she would do everything possible to ensure he was not the Republican Party’s presidential nominee in 2024.

Mr. Bouchard was first elected to the State Senate in 2017 to represent the Laramie County area. He is a gun-rights activist who owns a septic system cleaning business with his wife, according to his official biography.

Representative Tom Malinowski at a House Foreign Affairs Committee hearing in September. He is under scrutiny for profiting from trading medical and tech stocks at the height of the pandemic last year.
Stefani Reynolds for The New York Times

Representative Tom Malinowski, Democrat of New Jersey, on Friday defended a spate of lucrative stock trades he made last year as the economy reeled amid the coronavirus pandemic, after a report by The Associated Press suggested he had benefited financially from the crisis.

The trades involved as much as $1 million worth of securities in real estate, technology and medical companies whose work was affected by the pandemic. The A.P. said its review found that Mr. Malinowski, a second-term House member in a competitive district, staved off losses and profited handsomely through a string of well-timed trades, and used an oft-criticized practice known as short-selling, essentially making bets that companies would decline in value.

There is no suggestion that Mr. Malinowski’s trades were illegal or based on inside information he received as a member of Congress. But his investments began attracting scrutiny earlier this spring after the congressman, a longtime anti-corruption activist who previously worked at the State Department and Human Rights Watch, failed to publicly disclose some of his trading activity to Congress, as required. His political opponents have cited the trades to portray the congressman as unpatriotic and out of touch.

“The charge that Congressman Malinowski abused his office is categorically false,” his staff said in a lengthy statement on Friday responding to the report. Mr. Malinowski has conceded he made a mistake in failing to report his stock market activities, but has insisted that the individual trades were made entirely at the discretion of his financial advisers without his knowledge.

The Justice Department investigated a handful of senators last year for similar pandemic-era trading. But in those cases, investigators were studying whether lawmakers had acted on information shared in senators-only briefings or through other government connections, which may have been illegal. No one was ultimately charged.

Mr. Malinowski’s response on Friday included a statement from Gagnon Securities, his financial adviser, that said the transactions had been based exclusively on “publicly available information as well as proprietary analysis.”

Still, Mr. Malinowski’s political opponents were quick to criticize the congressman, saying he had acted cravenly to protect himself financially at a time when millions of Americans were out of work or watching their businesses fail. That line of attack is likely to follow him into the 2022 midterm election season, when Mr. Malinowski is likely to face a stiff Republican challenge.

“When Covid-19 hit, Tom Malinowski wasn’t rooting for American businesses to succeed, he was betting against them in the markets, shorting their companies, and hoping they’d fail to make big profits,” said Calvin Moore, a spokesman for the Congressional Leadership Fund, a Republican super PAC. “Tom Malinowski put himself and his own back pocket first, giving New Jersey voters every reason to show him the door.”

Though he denied wrongdoing, the congressman also tacitly acknowledged on Friday that the trades created an unseemly appearance for a public official. In a statement, his office said he was supportive of requiring members of Congress to put their assets in a blind trust and would do so himself going forward.

“Congressman Malinowski is committed to full transparency with the public,” his office said.

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The Biden administration announced on Friday that they will partner with a number of popular dating apps like Tinder, OkCupid, Hinge, BLK and Chispa, to promote vaccination status among single people.Alex Brandon/Associated Press

With a non-zero amount of awkwardness, the Biden administration on Friday highlighted a new plan to encourage more people to get vaccinated: an effort by a number of popular dating apps that will encourage pent-up young singles to promote their vaccination status, as the promise of a maskless summer grows tantalizingly within reach.

“We have finally found the one thing that makes us all more attractive: a vaccination,” Andy Slavitt, one of President Biden’s top coronavirus advisers, deadpanned during a virtual briefing for reporters. He later added, “In all seriousness, people are interested in other things in life besides their vaccine.”

Mr. Slavitt said that popular apps like Tinder, OkCupid, and Hinge — along with a suite of others, including BLK and Chispa, that cater to daters in specific communities — will add new features designed to reach a population of young people who may have been largely isolated from each other during the course of the pandemic, and will promote the idea that getting a shot could help users get a date. Tinder plans to launch a “Vaccine Center” to help users find nearby vaccination sites.

Highlighting the work of technology companies that can reach Americans where they are — on their phones — has been a cornerstone of the Biden administration’s efforts to combat access and hesitancy, and remind people who have not yet received a shot that doing so could help the country emerge from the pandemic. Providers are administering about 1.88 million doses per day on average, about a 44 percent decrease from the peak of 3.38 million reported on April 13, according to federal data.

Earlier this month, the president said that Uber and Lyft, two of the country’s largest ride-sharing services, would provide free rides to vaccination sites beginning May 24 and through July 4.

Mr. Slavitt said on Friday that the dating apps effort, which could reach over 50 million people in the United States, was not an official partnership with the companies. But the White House played a significant role in rallying them to participate, said an administration official, speaking on the condition of anonymity because the official was not authorized to comment publicly about the effort.

The Rev. Al Sharpton and Philonise Floyd, the brother of George Floyd, with other family members in Minneapolis last month.
Victor J. Blue for The New York Times

President Biden will host members of George Floyd’s family at the White House on May 25 to mark the first anniversary of his death, according to a senior administration official.

The visit will come more than a month after the former Minneapolis police officer Derek Chauvin was found guilty of murdering Mr. Floyd, who died after Mr. Chauvin knelt on his neck for more than nine minutes. Mr. Floyd’s death drew millions of protesters into the streets and spurred a national reckoning over race.

“It was a murder in the full light of day, and it ripped the blinders off for the whole world to see,” Mr. Biden said after the verdict was read. “For so many, it feels like it took all of that for the judicial system to deliver a just — just basic accountability.”

Mr. Biden has repeatedly called on Congress to pass an ambitious policing overhaul, known as the George Floyd Justice in Policing Act, by the anniversary of Mr. Floyd’s death.

“I know Republicans have their own ideas and are engaged in productive discussions with Democrats in the Senate. We need to work together to find a consensus,” Mr. Biden said during his address to a joint session of Congress last month. “But let’s get it done next month, by the first anniversary of George Floyd’s death.”

The bill’s future, though, remains uncertain. The bill has passed the House but has stalled in the Senate.

Representative Karen Bass, Democrat of California and the lead author of her party’s legislation, told reporters on Wednesday that lawmakers probably would not meet the May 25 deadline, but suggested that the measure could still be passed in the next few weeks.

Ms. Bass has been in quiet talks with Senator Tim Scott of South Carolina, Republicans’ lead emissary on the issue, to find a compromise. The chief sticking point has been Democrats’ demand to alter the legal liability shield for individual police officers, known as qualified immunity, to make it easier to bring civil lawsuits against them for wrongdoing.

The Democratic-controlled House passed the bill almost entirely along party lines in March, nearly a year after first passing it in 2020.

Katie Rogers contributed reporting.