Capping a day in which he appeared with two Democratic women in the running to be his vice president, Joseph R. Biden Jr. said on Thursday night that he did not remember Tara Reade, the woman who has accused him of sexual assault, and said that Americans “probably shouldn’t vote for me” if they believe the accusation, which he has strenuously denied.

“I think they should vote their heart,” he said on MSNBC, asked about his message to voters who had been inclined to support him but believed the Reade allegation. “I wouldn’t vote for me if I believed Tara Reade.”

Ms. Reade, a former Senate aide, has said that Mr. Biden assaulted her in 1993. After waiting for weeks to personally address her story, Mr. Biden did so earlier this month, though some allies and other progressives thought he should have taken on the issue more proactively, and sooner. In the interview on “The Last Word with Lawrence O’Donnell,” Mr. Biden said that women’s claims of assault should be taken seriously but should also be vetted, as he sharpened his questioning of Ms. Reade’s accusation.

“Look at Tara Reade’s story,” he said. “It changes considerably. But I don’t want to question her motive. I don’t want to question anything other than to say the truth matters.”

Also Thursday night, Mr. Biden indicated that he would not pardon President Trump if elected — “absolutely, yes, I commit,” he said, when asked if he would commit to not pardoning the president, and to the idea that no one is above the law.

And he said he had no involvement in the F.B.I. investigation of Michael T. Flynn, Mr. Trump’s former national security adviser. In his final days as vice president, Mr. Biden had been one of several officials who asked for the identity of an unnamed American mentioned in intelligence reports about contacts with Russians, an American who turned out to be Mr. Flynn, according to documents released this week by Republican senators.

“I was never a part, or had any knowledge, of any criminal investigation into Flynn while I was in office,” Mr. Biden said. “Period. Not one single time.”

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Credit…Butch Dill/Associated Press

Mr. Biden was joined for much of his MSNBC interview by Stacey Abrams, the 2018 Democratic nominee for governor of Georgia and a potential vice-presidential candidate, who has been open about her interest in the position. Earlier in the day, Gov. Gretchen Whitmer of Michigan — another possible running mate — joined a virtual round table with Mr. Biden.

Mr. Biden has pledged to run with a woman on the ticket, and the split-screen events illustrated, in some ways, the broader debate playing out in his camp and among his allies: whether Mr. Biden should select a woman of color, like Ms. Abrams, or prioritize regional considerations, like Ms. Whitmer’s ties to the industrial Midwest. He has said he is considering as many as a dozen candidates for the job.

“She has a great, great capacity to explain things, and to lay out exactly why it’s going to be so critically important in this election,” Mr. Biden said of Ms. Abrams, lauding her work on voting rights and calling her an “incredibly capable person.” Throughout the interview, Ms. Abrams praised Mr. Biden repeatedly, invoking his campaign trail language about restoring the soul of the nation and describing him as someone who “spent 40 years lifting up the cause of justice.”

A few hours earlier, he appeared with Ms. Whitmer and Philip D. Murphy of New Jersey and Ned Lamont of Connecticut, all Democratic governors, part of a day of virtual meetings with mayors and with the governors of three states hit hard by the coronavirus. He praised the officials on the front lines of the local response to the coronavirus and asked what they most needed from the federal government, positioning himself as a leader who could offer them the sort of support the current administration has not.

In an hourlong event, he peppered the governors with questions: What were they worried about? What did they need? Did they have enough personal protective equipment stockpiled to weather a resurgence of the virus in the fall if, as many public health experts expect, it does resurge?

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Credit…Pool, Michigan Governors Office, via Associated Press

If the conversation was granular at times, it spoke to the image of sober steadiness Mr. Biden has been trying to convey as he navigates the extraordinary challenge of simply staying visible, much less demonstrating leadership, during a pandemic that has shut down normal campaigning.

The governors are chief executives charged with managing a crisis, and Mr. Biden — who wants to be a chief executive charged with managing a crisis but has had little opportunity to show voters how he would do it — was aligning himself with them.

On Thursday evening, he and his wife, Jill Biden, also addressed a virtual gathering of his finance committee, where he indicated that he believes a growing number of battleground states are in play, and promised aggressive pushback to Mr. Trump in what he expects to be an extraordinarily ugly election, according to two participants. A Biden spokesman didn’t respond to a request for comment.

Mr. Biden is leading in the polls, both nationally and in key swing states. But the retail politicking Mr. Biden excels at is no longer possible, and unlike Mr. Trump — who is also missing his usual rallies — he does not have access to the daily platform of televised coronavirus news briefings, which Mr. Trump has often turned into de facto campaign events.