Biden dialed in to a call with worried members of his campaign team and told them he wasn't going anywhere, according to two sources familiar with the call. 

"No one is pushing me out. I'm not leaving. I'm in this race to the end," Biden said in a separate email blast by his campaign, urging supporters to "pitch in a few bucks" to help defeat his Republican rival Donald Trump in the Nov. 5 presidential election.

The president met virtually and in person with 24 Democratic governors and the mayor of Washington, D.C., on Wednesday evening to reassure them he is up to the job of standard-bearer for the party after the faltering debate performance.

Only three of the governors - the leaders of New York, Minnesota and Maryland - met with reporters afterwards, vowing to stand with Biden after what they called an honest discussion about his bad performance in last week's debate.

"The president has always had our backs. We're going to have his back as well," Maryland Governor Wes Moore said. 

Minnesota Governor Tim Walz, the chair of the Democratic Governors Association, said Biden's Thursday night debate performance against former President Trump was bad, but added that he felt Biden was fit for office.

Concerns about Biden's age and mental acuity exploded after Thursday's debate with Trump, in which the president mumbled under his breath, lost his train of thought at times and, at one point, talked of beating Medicare. The president has said that he was tired after two foreign trips and the White House has said he had a cold. 

Asked Wednesday if Biden was considering stepping down, White House press secretary Karine Jean-Pierre said: "Absolutely not." 

Soon after she spoke, two national polls suggested Biden's chances against Trump - who rattled off a series of well-worn falsehoods during the debate - had deteriorated. 

A Wall Street Journal survey found Trump beating Biden by a margin of 48 percent to 42 percent, up one percentage point, while a New York Times/Siena poll found Trump's lead over Biden had widened by three points to 49 percent to 43 percent. 

In a call among House Democrats on Wednesday, Arizona's Raúl Grijalva called for Biden to drop out of the race while Representative Seth Moulton from Massachusetts pointed toBiden's age as a liability.

“The unfortunate reality is that the status quo will likely deliver us President Trump,” Moulton said in a statement. "President Biden is not going to get younger.”

While the campaign has highlighted fundraising successes with grassroots donors and held damage control calls with donors, Reed Hastings, a major Democratic Party donor and a co-founder of streaming platform Netflix, called for Biden to step aside.

Vice President Kamala Harris has meanwhile gained support as his potential replacement. 

Dmitri Mehlhorn, an adviser to LinkedIn co-founder and Democratic megadonor Reid Hoffman, told Reuters his team would "enthusiastically support a ticket led by our tough and savvy vice president if Biden were to step aside for any reason."

Melhorn said Harris was the only serious national contender who had already been subjected to major attacks by Trump's "Make America Great Again" supporters.

"We would lose Joe's superpower brand, but we would gain other benefits and would still be competitive," he said.

Democrats and donors concerned about Biden's viability in the November election will be closely watching an interview with ABC News expected to be taped and aired Friday during a campaign visit to Madison, Wisconsin.

The White House said Biden has spoken with Democratic leaders in Congress as well as Democratic Representative Jim Clyburn, who was instrumental in Biden's 2020 win.

Clyburn, who has said he would back Harris as the presidential candidate if Biden stepped aside, told CNN on Wednesday that the party should hold a "mini-primary" if Biden steps aside, the first senior party member to talk publicly about how replacing Biden as a candidate could work.

Some of the governors who met with Biden on Wednesday could be potential rivals if pressure for him to step aside were to increase, but many of them also speak on Biden's behalf on the campaign trail.

Michigan Governor Gretchen Whitmer, California Governor Gavin Newsom, Illinois Governor J.B. Pritzker, Pennsylvania Governor Josh Shapiro and Kentucky Governor Andy Beshear have all been mentioned as possible replacements to Biden.