US President Joe Biden has hit back at criticism over his age, telling supporters in a fiery speech that he will win re-election in November after a poor debate performance fuelled fresh concern about his fitness.

“I know I’m not a young man, to state the obvious,” he told a rally in the battleground state of North Carolina on Friday, one day after he struggled in the televised showdown with his Republican rival Donald Trump.

“I don’t walk as easy as I used to… I don’t debate as well as I used to,” he acknowledged. “But I know what I do know, I know how to tell the truth [and] I know how to do this job.”

“I would not be running again if I didn’t believe with all my heart and soul that I could do this job,” Mr Biden, 81, added, as the cheering crowd in Raleigh chanted “four more years”.

Trump, meanwhile, held a rally of his own in Virginia just hours later, where he hailed a “big victory” in the debate which CNN said was viewed by 48m people on television and millions more online.

“Joe Biden’s problem is not his age,” the 78-year-old Trump said. “It’s his competence. He’s grossly incompetent.”

The former president dismissed speculation that Mr Biden would bow out of the race, saying he “does better in polls” that other Democrats, including California Governor Gavin Newsom and Vice-President Kamala Harris.

While questions over Mr Biden’s age are not new, his shaky performance on the debate stage – which was marked by verbal blanks, a hoarse voice and some difficult to follow answers – triggered panic among some Democrats who raised fresh questions about his candidacy.

Democratic officials, political operatives, and people close to the president who spoke to the BBC’s Katty Kay painted a picture of an anxious party that is concerned about the strength of their candidate.

Nancy Pelosi, the former Democratic House speaker, said that “from a performance standpoint it wasn’t great.” Other Democrats, such as Kate Bedingfield, Biden’s former communications director, called it “a really disappointing debate performance”.

Democratic donors who spoke anonymously to various media outlets were more forthright, with one calling the performance “disqualifying”. “The only way it could have been more disastrous was if he had fallen off the stage. Big donors are saying… he has to go,” one Democratic operative told the Financial Times.

But publicly, many senior Democrats and Biden allies defended his performance as they sought to calm the concern on Friday. Among those to rally behind Mr Biden were former President Barack Obama, who tweeted that “bad debate nights happen”.

“This election is still a choice between someone who fought for ordinary folks his entire life and someone who only cares about himself,” Mr Obama wrote, adding that Mr Trump is “someone who lies through his teeth for his own benefit”.

Mr Biden and his campaign were quick to dismiss calls for him to step down as the candidate. “President Biden is the only person who has ever beaten Donald Trump. He will do it again,” a campaign adviser said. “This election was never going to be won or lose in one rally, one conversation, or one debate. “

The Biden campaign also said the president had raised $14m from fundraisers in recent days, in an apparent effort to show it was maintaining momentum. Mr Biden is expected to meet with donors on Friday and Saturday, including at events in Manhattan and the wealthy Hamptons.