US President Joe Biden vowed to stay in the 2024 presidential race during a call with campaign staff on Wednesday (Jul 3) and insisted in meetings with Democratic lawmakers and governors that he is fit for reelection despite his shaky debate performance last week.

Biden dialled into 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 an email blast by his campaign, urging supporters to "pitch in a few bucks" to help defeat his 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, DC 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 on 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 per cent to 42 per cent, up one percentage point, while a New York Times/Siena poll found Trump's lead over Biden had widened by three points to 49 per cent to 43 per cent.

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 to Biden'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.”