President Biden told a gathering of Democratic governors that he needs to get more sleep and work fewer hours, including curtailing events after 8 p.m., according to two people who participated in the meeting and several others briefed on his comments.

The remarks on Wednesday were a stark acknowledgment of fatigue from the 81-year-old president during a meeting intended to reassure more than two dozen of his most important supporters that he is still in command of his job and capable of mounting a robust campaign against former President Donald J. Trump.

Mr. Biden’s comments about needing more rest came shortly after The New York Times reported that current and former officials have noticed that the president’s lapses over the past few months have become more frequent and more pronounced.

But Mr. Biden told the governors, some of whom were at the White House while others participated virtually, that he was staying in the race.

He described his extensive foreign travel in the weeks before the debate, something that the White House and his allies have in recent days cited as the reason for his halting performance during the debate. Initially, Mr. Biden’s campaign blamed a cold, putting out word about midway through the debate amid a series of social media posts questioning why Mr. Biden was struggling.

Mr. Biden said that he told his staff he needed to get more sleep, multiple people familiar with what took place in the meeting said. He repeatedly referenced pushing too hard and not listening to his team about his schedule, and said he needed to work fewer hours and avoid events scheduled after 8 p.m., according to one of the people familiar with what took place at the meeting.

After Gov. Josh Green of Hawaii, a physician, asked Mr. Biden questions about the status of his health, Mr. Biden replied that his health was fine. “It’s just my brain,” he added, according to three people familiar with what took place — a remark that some in the room took as a joke, including Gov. Kathy Hochul of New York, according to a person close to her. But at least one governor did not, and was puzzled by it.

Jen O’Malley Dillon, Mr. Biden’s campaign chair, who attended the meeting, said in a statement that he had said, “All kidding aside,” a recollection confirmed by another person briefed on the meeting. Ms. O’Malley Dillon added: “He was clearly making a joke.”

Kevin Munoz, a spokesman for the Biden campaign, said of the president’s comments about more sleep and less late work: “President Bush went to bed at 9, and President Obama made dinner at 6:30. Normal presidents strike a balance, and so does Joe Biden. Hardly the same rigor as Donald Trump who spends half of his day ranting on Truth Social about plans that would cause a recession and other half golfing.”

Mr. Biden took two foreign trips in the weeks before the debate, but then spent a week in debate preparation at Camp David with a group of advisers. One person close to Mr. Biden said that his comment about sleep and work hours reflected the fact that during the practice sessions, which came immediately after the foreign trips, he was engaged in a lot of official work on top of the campaign activity.

Multiple governors who participated in the meeting expressed dismay afterward that there had been little debate about whether Mr. Biden should continue his 2024 presidential campaign — a topic they discussed at length during a call the governors held among themselves on Monday.

Despite some of their private trepidations about Mr. Biden continuing his campaign, none of the governors — some of whom are mentioned as possible Biden successors — directly said that he should drop out of the race, according to multiple people briefed on the meeting.

Gov. J.B. Pritzker of Illinois, a staunch Biden supporter, asked early in the meeting about the president’s plan going forward in the campaign, according to two people briefed on the meeting.

Others who were part of the meeting were pointed in their comments. Speaking toward its end, Gov. Jared Polis of Colorado, who attended virtually, told the president that he had heard a groundswell of wishes from various people that Mr. Biden would end his campaign, according to two people who were briefed on the call.

Two other governors, Janet Mills of Maine and Michelle Lujan Grisham of New Mexico, also voiced concerns. Ms. Mills said that people didn’t think Mr. Biden was up to running, and Ms. Lujan Grisham said she was worried that the president could lose her state, according to two of the people briefed.

Speaking for themselves, some governors have been more vocal. Gov. Maura Healey of Massachusetts, though she did not speak during the Wednesday meeting with Mr. Biden, said during a Monday call with fellow governors about the situation that she had told Jeff Zients, the White House chief of staff, that the president’s political position was “irretrievable” after his disastrous debate performance, according to two people who were on that call.

Mr. Biden has acknowledged to two allies that he knows he may not be able to save his candidacy for a second term if he can’t demonstrate his abilities to voters following the debate. He sought to reassure concerned campaign aides in a call on Wednesday before the meeting with the governors, saying he was in the race to stay.

But the fact that Mr. Biden began the conversation with the governors by declaring that he was continuing on left some participants feeling that any further discussion about the state of play was chilled.

Mr. Biden told a Milwaukee radio station in an interview made public Wednesday that he had “a bad night.” In the prerecorded interview with the radio host Earl Ingram, Mr. Biden added, “The fact of the matter is that I screwed up. I made a mistake.”

Mr. Biden also told the governors that he had been examined by his physician at some point in the days after the debate because of the cold he was suffering from and that he was fine, multiple people familiar with what took place said. Politico reported earlier on Mr. Biden’s checkup, which the White House said took place on Monday, was brief and wasn’t a full physical examination.

A White House spokesman, Andrew Bates, confirmed that Mr. Biden had seen the White House physician to check on the cold. But on Friday, the White House press secretary, Karine Jean-Pierre, said the opposite, telling reporters that Mr. Biden had not had any kind of medical checkup since February.

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