A new poll suggests that some Democratic voters are increasingly concerned about whether Joe Biden is mentally fit to serve as president after a shaky debate performance on Thursday.

A CBS News/YouGov poll released on Sunday indicated that 72% of registered voters believe the president does not have the mental and cognitive health to serve as president - a sharp increase from the 65% who said the same in an earlier poll.

Forty-nine percent of voters said the same of former President Donald Trump.

Particularly alarming for the Biden campaign, 45% of registered Democrats who responded to the poll said they believe the president should step aside for another candidate.

Concerns about the candidates' age - Mr Biden's is 81 and Trump is 78 - existed before Thursday's debate. Mr Biden's hoarse voice and muddled answers, however, renewed concerns among some Democrats about his candidacy and left some calling for Mr Biden to step aside.

The president's family encouraged him to stay in the race and keep fighting during a long-planned visit to Camp David on Sunday, a source with knowledge of the conversations confirmed to CBS News, BBC's US partner.

Still, Maryland Congressman Jamie Raskin, a Democrat and White House ally, called it a "difficult situation" in an interview with MSNBC on Sunday.

He said that there are "very honest and serious and rigorous conversations taking place at every level of our party", though he emphasised that the ultimate decision remained Mr Biden's.

“Regardless of what President Biden decides, our party is going to be unified and our party also needs him at the very centre of our deliberations in our campaign," he added.

In the days since the debate, first lady Jill Biden, Vice President Kamala Harris and former President Barack Obama have publicly acknowledged it was not Mr Biden's best performance.

But they and many other Democratic allies rejected calls that Mr Biden should step aside.

House Minority Leader Hakeem Jeffries told MSNBC on Sunday that the president's debate performance "was a setback. But, of course, I believe a setback is nothing more than a setup for a comeback".

This poll from CBS News and polling organisation YouGov contrasts with a memo shared by Biden campaign chairwoman Jen O’Malley on Saturday. It claims that internal polling shows that it is the "beltway class" counting Mr Biden out, not Americans across the country.

When asked about the new poll, Biden administration officials argued head-to-head polls matter more and show the president leading by a point or tied with Trump.

“The grassroots is not fundamentally panicking like the Beltway is when you look at the head-to-heads,” an unnamed Biden administration official told CBS News. “Before Thursday, there were people who thought he was too old, but a lot of those people were still picking him over Trump.”

But interviews with voters after the debate, back up the concern expressed in CBS News' poll. Voters told BBC News they were worried about the president after his performance.

"I am less confident in the ability of Biden to lead this country today than I ever have been," one Democratic voter told the BBC after the debate.

With concerns growing, the president's campaign surrogates appeared on a series of politics shows in the US on Sunday morning.

Democratic Senator Chris Coons, a close ally of the president and a campaign co-chair, fiercely defended the president on ABC News' This Week.

“Joe Biden has an incredible record, and he knows, as the American people do, that when you get knocked down, you get back up and you fight harder," the senator said. "That’s what he’s planning to do.”

When Mr Coons was asked about the president's mental fitness, he deflected and raised concerns about Trump. He also would not say whether Mr Biden was listening to the growing concerns about his age and stability.

"He's the only Democrat who can beat Donald Trump," Mr Coons said about the president.

Democratic Senator Raphael Warnock said on NBC News Meet the Press that the president should "absolutely not" drop out of the race.

"There have been more than a few Sundays when I wished I preached a better sermon" Mr Warnock, who is also a pastor, said.

"But after the sermon was over, it was my job to embody the message, to show up for the people that I serve. And that's what Joe Biden has been doing."

Meanwhile, Republicans doubled-down on their critiques of the president's performance saying it showed why Trump was the right choice.

"Joe Biden had a disastrous performance, which is why they're talking about replacing him," Republican Senator JD Vance said on Fox News on Sunday.

Mr Vance said Trump was engaging, funny and had a "good natured demeanour" during the debate.

"That's what you need to be able to serve as president of the United States and to contrast with Joe Biden, who seemed to be unable to complete a sentence," he said.