The remark from Biden came during a private call with donors last week as the Democrat was scrambling to shore up his imperilled candidacy with key party constituencies.
During that conversation, Biden declared he was 'done' talking about his poor debate performance and it was 'time to put Trump in the bull's-eye,' saying there'd been too little scrutiny of his rival's stances and rhetoric.
"It was a mistake to use the word," Biden told NBC anchor Lester Holt in a clip released by the network, ahead of its broadcast on Monday.
Biden continued: "How do you talk about the threat to democracy which is real, when a president says things like he says? Do you just not say anything because it may incite somebody?"
The president said he was not the one who engages in 'that rhetoric,' referring to Trump's past comments about a 'bloodbath' if the Republican loses to Biden in November.
Meanwhile, Biden described the Republicans vice-presidential pick, Ohio Senator JD Vance, as a 'clone', as he prepares to resume full-throttle campaigning after Trump survived an assassination attempt.
Vance, 39 received the party's formal nomination at its national convention in Milwaukee shortly after Trump announced his choice.
"He's a clone of Trump on the issues," Biden told reporters at Andrews Air Force Base shortly before departing for Nevada for a series of speeches and campaign events. "I don't see any difference."
The NBC interview had been scheduled before the attempt on Trump's life at a rally in Pennsylvania,.
It had been part of Biden's broader strategy to prove his fitness for office after angst grew among Democrats because of his disastrous June 27 debate performance.
In the immediate aftermath of the assassination attempt on Saturday, the Biden campaign hit pause on messaging.
Hours ahead of the NBC interview, his campaign issued a blistering statement on Trump's selection of Ohio Senator JD Vance as his running mate, saying he picked the freshman senator because he would "bend over backwards to enable Trump and his extreme MAGA agenda."
"Over the next three and a half months, we will spend every single day making the case between the two starkly contrasting visions Americans will choose between at the ballot box this November," said Biden campaign chairwoman Jen O'Malley Dillon.
Biden has acknowledged that his candidacy and agenda will be under attack at the Republican National Convention this week, and aides feel no need to put their campaign on complete pause while Biden comes under scrutiny in Milwaukee.
But they'll tread carefully in the aftermath of the shooting at the Trump rally in Butler, Pennsylvania.
"I'll be travelling this week, making the case for our record and the vision — my vision of the country — our vision," Biden said during his Oval Office remarks on Sunday night, just the third such address of his presidency. "I'll continue to speak out strongly for our democracy, stand up for our Constitution and the rule of law, to call for action at the ballot box, no violence on our streets. That's how democracy should work."
Biden's renewed campaigning this week comes as Democrats have been at an impasse over whether the incumbent president should continue in the race even as he was defiant that he would stay in. Biden has made it clear in no uncertain terms that he remains in the race, and aides have been operating as such.
The attempt on Trump's life appears to have stalled some of the momentum of efforts to urge Biden to step aside.
