US President Joe Biden defended both his "mental acuity" and his rhetoric about Donald Trump Monday, in a second TV interview aimed at ending calls for him to quit his re-election bid following a disastrous debate.

The 81-year-old delivered an often combative defence of his mental and physical fitness for office during the one-on-one with broadcaster NBC, which nevertheless featured some of the word salads that have worried Democrats.

"I'm old," Biden told host Lester Holt in the interview at the White House. "But I'm only three years older than Trump, number one. And number two, my mental acuity has been pretty damn good."

He added: "I understand why people say, 'God, he's 81 years old. Whoa. What's he gonna be when he's 83 years old, 84 years?' It's a legitimate question to ask."

Biden's interview was the latest attempt by the White House to assuage growing fears over the Democrat's age and mental state following the dismal debate performance on June 27.

The sit-down was announced last week, before the assassination attempt on Republican candidate Donald Trump on Saturday -- which inevitably became a key subject of the interview.

Biden told Holt he was wrong when he recently told donors it was "time to put Trump in the bullseye" of his election campaign.

"It was a mistake to use the word," Biden said when asked if he had gone too far with his rhetoric as a deeply polarised nation reels from the shooting, in which Trump's ear was injured. "I meant focus on him, focus on what he's doing," Biden said.

But Biden doubled down on what he said was the need to "talk about the threat to democracy" posed by former president Trump.

"Look, I'm not the guy that said 'I want to be a dictator on Day One,'" he said, referring to remarks by Trump that alarmed many people.

Several prominent Republicans, including Trump's newly announced running mate J D Vance, have since accused Biden of having responsibility for the assassination attempt because of his language against Trump.

The allegations -- themselves often incendiary -- come as authorities have said they've yet to identify the shooter's ideology, and even as Republicans themselves often use guns in their political imagery.

The interview screened just an hour before Trump took to the stage with a bandage on his ear at the Republican National Convention in Milwaukee, his first public appearance since the shooting.