Mr Biden held a closed-door lunch with Vice-President Kamala Harris at the White House as speculation mounted over whether she would replace him as the party’s candidate in November’s election.
The pair then joined a call with the broader Democratic campaign where Mr Biden made clear he would remain in the race and Ms Harris reiterated her support. “I’m the nominee of the Democratic Party. No one’s pushing me out. I’m not leaving,” he told the call, a source told BBC News.
That same phrase was repeated in a fundraising email sent out a few hours later by the Biden-Harris campaign. “Let me say this as clearly and simply as I can: I’m running,” Mr Biden said in the email, adding that he was “in this race until the end”.
Questions have been swirling around whether the 81-year-old will continue with his campaign following the debate with Trump, which was marked by verbal blanks, a weak voice and some answers which were difficult to follow. It sparked concern in Democratic circles around his fitness for office and his ability to win the election.
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Pressure on Mr Biden to drop out has only grown in the days since as more polls indicate his Republican rival’s lead has widened. A New York Times poll conducted after the debate, which was published on Wednesday, suggested Trump was now holding his biggest lead yet at six points.
And a separate poll published by the BBC’s US partner CBS News suggested Trump has a three-point lead over Biden in the crucial battleground states. That poll also indicated the former president was leading nationally.
The damaging polling has been compounded by some Democratic donors and lawmakers publicly calling on the president to stand aside. Ramesh Kapur, an Indian-American industrialist based in Massachusetts, has organised fundraisers for Democrats since 1988.
“I think it’s time for him to pass the torch,” Mr Kapur told the BBC. “I know he has the drive, but you can’t fight Mother Nature.”
And two Democrats in Congress also called for a change at the top of the party’s ticket. The latest, Representative Raul Grijalva of Arizona, told the New York Times it was time for Democrats to “look elsewhere”.
Despite this, the White House and the Biden campaign have vehemently denied reports he is actively weighing his future and say he is committed to defeating Trump for a second time on 5 November.
The New York Times and CNN reported on Wednesday that Mr Biden had told an unnamed ally he was evaluating whether to stay in the race.
Both reports said the president had told the ally he was aware his re-election bid was in danger and his forthcoming appearances – including an ABC News interview and a Friday rally in Wisconsin – were hugely important to his campaign.
A spokesperson rejected the reports as “absolutely false”, shortly before White House Press Secretary Karine Jean-Pierre faced a barrage of questions about Mr Biden’s commitment to the race.
She said the reports that he may drop out were untrue: “We asked the president [and] the president responded directly… and said ‘no, it is absolutely false’. That’s coming directly from him.”
On a call with White House staff on Wednesday, chief of staff Jeff Zients urged them to keep their “heads down”, according to CBS News.
“Get things done. Execution. Execution. Execution” he said.
“There is so much to be proud of, and there is so much more we can do together under this President’s leadership.”
Mr Biden met 20 Democratic governors from around the country, including California’s Gavin Newsom and Michigan’s Gretchen Whitmer, later on Wednesday. Both have been tipped as potential replacements if Mr Biden were to stand aside.
“The president has always had our backs, we’re going to have his back as well,” Maryland Governor Wes Moore told reporters after the meeting.
New York Governor Kathy Hochul said the two dozen governors who had just met the president pledged their support and that Mr Biden had vowed he was “in it to win it”.
But Ms Harris is still considered the most likely replacement. The 59-year-old has been hampered by poor approval ratings, but her support has increased among Democrats since the Biden-Trump debate.
The vice-president gave an immediate interview on CNN after the debate, projecting calm as she expressed full support for the president.
“She’s changing nothing,” a source close to Ms Harris told BBC News, adding that she would continue to hit the road on behalf of the campaign.
“She has always been mindful to be a good partner to the president,” said Jamal Simmons, Ms Harris’ former communications director.
“The people who ultimately will make the decision about who the nominee should be mostly are people who are pledged to him. Her best role is to be a partner to him.”
Members of the Democratic National Committee are charged with voting to officially make President Biden the party’s nominee at the August convention, putting him on the ballot nationwide.
One member, who has spoken to other delegates and requested anonymity to speak frankly about sensitive discussions, told the BBC that the nomination should go to Vice-President Harris if Mr Biden opted not to run.
“If we open up the convention, it will cause pure chaos that will hurt us in November,” they said.
A report by the Washington Post, meanwhile, said Mr Biden and his team recognised that he must demonstrate his fitness for office in the coming days.
He appeared at a Medal of Honor ceremony on Wednesday and has planned trips to Wisconsin and Philadelphia later in the week.
