U.S. President Joe Biden said on Friday he intended to defeat Republican rival Donald Trump in the November presidential election, giving no sign he would consider dropping out of the race after a feeble debate performance that dismayed his fellow Democrats.

"I know I'm not a young man, to state the obvious," an ebullient Biden said at a rally one day after the head-to-head showdown with his Republican rival, which was widely viewed as a defeat for the 81-year-old president.

"I don't walk as easy as I used to, I don't speak as smoothly as I used to, I don't debate as well as I used to," he said, as the crowd chanted "four more years."

"I would not be running again if I didn't believe with all my heart and soul that I could do this job. The stakes are too high," Biden said.

Biden's verbal stumbles and occasionally meandering responses in the debate heightened voter concerns that he might not be fit to serve another four-year term and prompted some of his fellow Democrats to wonder whether they could replace him as their candidate for the November 5 U.S. election.

Campaign spokesperson Michael Tyler said there were no conversations taking place about that possibility. "We'd rather have one bad night than a candidate with a bad vision for where he wants to take the country," he told reporters aboard Air Force One.

The campaign held an "all hands on deck" meeting on Friday afternoon to reassure staffers that Biden was not dropping out of the race, according to two people familiar with the meeting.

At an afternoon rally in Chesapeake, Virginia, Trump told supporters that he had a "big victory against a man looking to destroy our country."

"Joe Biden's problem is not his age," Trump said. "It's his competence."

Trump advisers said they thought the debate would bolster their chances in Democratic-leaning states like Virginia, which has not backed a Republican presidential candidate since 2004.

Questions about Trump's fitness for office have also arisen over his conviction last month in New York for covering up a hush money payment to a porn star, his efforts to overturn the 2020 election and his chaotic term in office.

He is scheduled to be sentenced on July 11, just days before his party convenes to formally nominate him. He still faces three other criminal indictments, though none appear likely to reach trial before November.

Biden's shaky performance in the debate drew stunned global reactions on Friday, prompting public calls for him to step aside and likely leaving some of America's closest allies steeling for Trump's return.