On the first night of their convention, Republicans appealed to “quiet neighborhoods” by warning of vengeful mobs of “anarchists.” Twenty-four hours later, Mr. Trump and his party cast the president as the country’s greatest protector — not only from mobs of protesters but also of free speech, economic opportunity and even faith itself.

“This is a fight for freedom versus oppression,” said Tiffany Trump, the president’s younger daughter. “A fight to keep America true to America.”

Speaker after speaker extolled the president as steady steward of the country’s promise, casting Democrats as radical leftists intent on destroying the American way of life.

The message seemed tailored to suburban voters — the people who were instrumental in Mr. Trump’s win in 2016. It built on the previous evening’s effort to convince those voters that the president wasn’t racist, despite years trafficking in racist tropes and nicknames.

On Tuesday night, his campaign wanted viewers to know that he was not anti-immigrant or sexist, either.

“To mothers and parents everywhere, you are warriors,” said Melania Trump, the first lady. “In my husband, you have a president who will not stop fighting for you and your families.”

Anti-abortion activists praised the president for his steps to limit access to abortion. A dairy farmer from Wisconsin, a lobster fisherman from Maine and a mayor from Minnesota’s Iron Range cast Mr. Trump as saving their economic livelihoods. Nick Sandmann, a Covington Catholic High School graduate and the focus of a viral video from last year, applauded the president’s war on so-called “cancel culture” and the mainstream media.

Mr. Trump’s own son, Eric, put it the most bluntly, promising “every proud American who bleeds red, white and blue, my father will continue to fight for you.”

ImagePresident Trump and the first lady, Melania Trump, after her speech in the White House Rose Garden on Tuesday.
Credit…Doug Mills/The New York Times

The tone was far more uplifting than the dark dystopia painted by speakers the previous night, featuring heartwarming friendships between FBI investigators and reformed criminals, police officers and drug addicts.

Amid sunny promises for the future, the illness and economic devastation of the coronavirus was barely acknowledged until the first lady’s address at the end of the program, nor were the nearly 180,000 Americans who have died from Covid-19.

In his remarks, Larry Kudlow, the president’s top economic adviser, pointedly spoke of the pandemic using the past tense.

“It was awful,” Mr. Kudlow said in a video address. “Hardship and heartbreak were everywhere. But presidential leadership came swiftly and effectively with an extraordinary rescue for health and safety to successfully fight the Covid virus.”

Mrs. Trump promised that her husband would not stop fighting until a treatment for the virus became widely available, comments that were a notable break from the standard rhetoric of the president and his administration that seek to downplay the virus.

“Donald will not rest until he has done all he can to take care of everyone impacted by this terrible pandemic,” Mrs. Trump said in her address, which was delivered live from the Rose Garden.

Much of the evening was devoted to recasting the president’s image as an inclusive leader, welcoming to immigrants, eager to promote women and embracing of racial diversity. The president was happy to play his part, issuing a presidential pardon for convention viewers and hosting a naturalization ceremony at the White House.

Mr. Trump welcomed five new citizens he described as “absolutely incredible people into our great American family.”

“You followed the rules, you obeyed the laws,” he said. “You learned your history, embraced our values and proved yourselves to be men and women of the highest integrity.”

Suburban white voters, and particularly suburban white women, remained the heart of the convention’s appeal. Mrs. Trump spoke about the impact of women’s voices “in our nation’s story.” A video featuring the women working in the White House highlighted Mr. Trump’s qualities as a boss.

“The level of genius is unbelievable, frankly,” Mr. Trump — who has been accused of sexual assault and misconduct by more than a dozen women and was caught on tape bragging about forcing himself on women — said in a recorded segment.

“This president has been a champion for women, mostly because he speaks to them as if they can handle and tackle all issues,” said Kellyanne Conway, President Trump’s counselor and one of his longest-serving aides. (Ms. Conway announced on Sunday that she was leaving the White House to focus on her children.)

And Kimberly Guilfoyle, a former Fox News host, praised Mr. Trump for treating women equally in the workplace. “I don’t want a job because of my gender, I want the job because I’m the best person for that position. That’s it,” said Ms. Guilfoyle, who is now dating Mr. Trump’s son, Donald Trump Jr. “And he respects that.”

Republicans broadcast their convention from an imposing, columned auditorium in Washington, but they want the message to resonate in the suburbs. Places where, in their telling, Americans are hunkered down, terrified of “radical left Democrats” intent on “taking away the American dream.”

Republicans have lost the suburbs only three times since 1980: In 1992, 1996 and 2008 — all three, Democratic presidential wins. Even in those races, the G.O.P. candidate lost by no more than five points. In 2016, suburbs powered Mr. Trump’s victory, with exit polls showing he won them by four points.

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Credit…Pete Marovich for The New York Times

An ABC News/Washington Post poll released in July shows Joseph R. Biden Jr. leading Mr. Trump in the suburbs by a margin of nine percentage points. Another survey by Fox News found an 11-point advantage for the former vice president.

Mr. Trump won the suburbs of North Carolina by 24 points, according to 2016 exit polls. He’s now losing them by 21 points, according to a Fox News poll in June. In Florida, a state that was expected to favor Mr. Trump, a 10-point advantage in 2016 exit polls is now a six-point deficit.

The president’s attempts to shore up support among white suburban voters by playing on racist fears began in earnest this summer, when he moved to eliminate an Obama-era program intended to combat racial segregation in suburban housing, claiming the program had a “devastating impact on these once thriving Suburban areas.”

During the first opening of the R.N.C., much of the appeal to these voters was also cloaked in retrograde racial tropes, a return to a brand of Republican identity politics with deep roots in the conservative movement. In the midst of the social unrest of 1968, President Richard Nixon’s so-called Southern strategy focused on a law and order message — a phrase lifted by Mr. Trump and tweeted dozens of times as racial justice protests spread across the country this spring and summer.

On Monday night, Charlie Kirk, the founder of a conservative student group, praised Mr. Trump as “the bodyguard of western civilization,” a phrase generally used among white supremacists as code for white identity. Vernon Jordan, a Democratic state representative from Georgia, accused Democrats of keeping Black voters on a “mental Plantation.”

Race played little role on Tuesday evening, even as demonstrations and destruction rocked the city of Kenosha, Wis., after police there shot Jacob Blake, a Black man, in front of his three young children.

Shortly before the start of his convention, Mr. Trump tweeted that the National Guard should be called into the city to control the demonstrations and destruction that have rocked the city — a step already taken by the Democratic governor. An opening prayer was the only mention of Mr. Blake.

Still, echoes of Mr. Nixon pervaded the proceedings, the former president’s “silent majority” becoming the “forgotten man.” In the Trump campaign’s telling, those are the working men and women who elected him to the White House four years ago.

“I’m proud to watch you give them hell,” said the younger Mr. Trump, directly addressing his remarks to his father. “You are making America proud again. And yes, together, with the forgotten man and woman who are finally forgotten no more, you are making America great again.”