Democratic President Joe Biden's family has urged him to ignore calls to step aside following his disastrous debate against Republican Donald Trump.

He spent Sunday with relatives at a presidential retreat where they encouraged him to keep fighting, according to the BBC's US partner CBS News.

Anxiety has gripped sections of his party following a rambling and at times incoherent performance in Atlanta.

Polls since then suggest concerns about his age - he is 81 - have increased.

A CBS News/YouGov poll released on Sunday indicated that 72% of registered Democratic voters believe the president does not have the mental and cognitive health to serve as president. Nearly half said he should step aside.

But the message from his campaign team and his family is that he remains the party's best hope to defeat Trump.

The family gathering at Camp David in Maryland had been previously scheduled as a photoshoot by celebrity photographer Annie Leibovitz. Mr Biden's wife Jill, his children and grandchildren were among those present.

Jill Biden told Vogue magazine in a phone call from Camp David that they “will not let those 90 minutes define the four years he’s been president".

They would continue fighting, she said, adding that her husband “will always do what’s best for the country”.

The encouragement of the family to stay the course was first reported by the New York Times and later confirmed by CBS News.

Some relatives have reportedly blamed his poor performance on over-preparation by his aides. A person close to Jill Biden told CBS she was not among those criticising his team.

Concerns about the age of both candidates - Mr Biden is only three years older than Trump who is 78 - were present before Thursday's debate.

But Mr Biden's weak voice and muddled answers renewed concerns about his candidacy and left some calling for him to step aside.

The New York Times editorial board said in an opinion piece that the "greatest public service [Biden] can now perform is to announce that he will not continue to run for re-election".

Trump was also criticised for his performance - he made a number of false assertions including his long-held grievance that the 2020 election was stolen from him.

On Sunday, top Democrats appeared on the morning shows to defend the president.

"When you get knocked down, you get back up and you fight harder," said Senator Chris Coons.

Maryland congressman Jamie Raskin did entertain the notion that Mr Biden might not be the candidate come the Democratic convention in August when the presidential nominee will be crowned.

"Whether he's the candidate or someone else is the candidate, he's going to be the keynote speaker at our convention. He will be the figure that we rally around to move forward," said Mr Raskin.

Republicans said the debate 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.

If Mr Biden did step aside, it is possible that the Democratic Party could launch a search for a new candidate in time for the convention but it is not a straightforward process.