President Joe Biden told NBC News in an interview on July 15 that it was a “mistake” to say he wanted to put a “bull’s-eye” on Republican nominee Donald Trump, but argued that the rhetoric from his opponent was more incendiary while warning that Mr. Trump remained a threat to democratic institutions.

Those remarks from Mr. Biden came during a private call with donors last week as the Democrat had been scrambling to shore up his imperilled candidacy with key party constituencies. During that conversation, Mr. Biden declared that he was “done” talking about his poor debate performance and that it was “time to put Mr. Trump in the bull’s-eye,” saying Mr. Trump has gotten far too little scrutiny on his stances, rhetoric and lack of campaigning.

The NBC interview came as Mr. Biden and his reelection team prepared to resume full-throttle campaigning after a brief pause following the weekend assassination attempt on Mr. Trump. The President and his campaign let loose a flurry of criticism after the GOP nominee announced freshman Sen. J.D. Vance of Ohio as his running mate.

“He’s a clone of Mr. Trump on the issues,” Mr. Biden told reporters as he headed to Nevada for a series of speeches and campaign events. “I don’t see any difference.”

Once Mr. Vance was tapped as Mr. Trump’s vice-presidential pick, the Biden campaign hit send on a fundraising solicitation signed by the President, and his team issued a blistering statement, saying he picked the freshman senator because he would “bend over backwards to enable Trump and his extreme MAGA agenda.” For her part, Vice President Kamala Harris phoned Mr. Vance to congratulate him and left him a voicemail message, according to a person familiar with the matter.

And to NBC anchor Lester Holt, Mr. Biden made it clear that he would keep up his focus on Trump. While he acknowledged his “mistake,” Biden nonetheless said he is “not the guy who said I wanted to be a dictator on day one” and that he wanted the focus to be on what Mr. Trump was saying. It’s Mr. Trump, not Mr. Biden, who engages in that kind of rhetoric, Mr. Biden said, referring to Trump’s past comments about a “bloodbath” if the Republican loses to Mr. Biden in November.

“Look, how do you talk about the threat to democracy, which is real, when a President says things like he says?” Mr. Biden said. “Do you just not say anything because it may incite somebody?”

The NBC interview, scheduled before the attempt on Mr. Trump’s life at a rally in Pennsylvania, had been part of Mr. Biden’s broader strategy to prove his fitness for office after angst grew among Democrats because of his disastrous June 27 debate performance.

The Biden campaign recalibrated some of its political plans in the immediate aftermath of the assassination attempt on July 13, pulling advertising off the air and hitting pause on messaging. The White House also scrapped Mr. Biden’s planned July 15 visit to the Lyndon B. Johnson library, where he had been slated to deliver remarks on civil rights.

Mr. Biden also spoke privately to Mr. Trump after the assassination attempt, a call that the President described in the NBC interview as “very cordial.”

“I told him how concerned I was and wanted to make sure I knew how he was actually doing,” Mr. Biden said. “He sounded good. He said he was fine and he thanked me for calling. I told him it was literally in the prayers of Jill and me, and I hoped his whole family was weathering this.”

It’s still not finalized when Mr. Biden’s campaign ads will resume airing. But Mr. Biden is pressing on with the Nevada portion of his previously scheduled western swing, which will include remarks to the NAACP and UnidosUS, a Latino civil rights and advocacy group. He’ll also headline what’s been billed as a “campaign community event” on July 17 in Las Vegas.

Mr. Biden has acknowledged that his candidacy and agenda will be under attack at the Republican National Convention this week, and aides had felt no need to halt their campaign completely, particularly while Mr. Biden comes under scrutiny in Milwaukee.

Asked whether Mr. Biden would adjust his messaging this week in light of the assassination attempt, O’Malley Dillon pointed to his Oval Office address as a “roadmap for the whole country,” which she said was no different than Mr. Biden’s broader message from the start of his candidacy.

“You’re going to hear the President continue to make his affirmative agenda clear,” she said. “Not just in abstract terms, but very specifically on how it continues to help the American people versus this very negative point of view and extreme agenda that the American people have already said that they don’t want.”

Mr. 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. Mr. Biden has made it clear in no uncertain terms that he remains in the race, and aides have been operating as such.

It was unclear if the attempt on Mr. Trump’s life would blunt Democratic efforts to urge Biden to step aside, but it appears to have stalled some of the momentum, for now. No Democrats have called for him to exit the race since the shooting Saturday night.

In the hours before the shooting, Mr. Biden was still being confronted by frustration and scepticism from Democratic lawmakers. Rep. Jared Huffman of California said he asked the president during his meeting with the Congressional Progressive Caucus about objectively assessing the trajectory of the race, and if the Lord almighty doesn’t intervene would Mr. Biden consider “the best earthly alternative”: meeting with former Presidents Obama and Clinton, Democratic leadership including Rep. Hakeem Jeffries and Sen. Chuck Schumer, and former Speaker Nancy Pelosi “to seek their advice.”

Mr. Huffman said on a social media post that Mr. Biden “disagreed with the notion that we are on a losing trajectory.”

And while Mr. Biden expressed a “willingness to listen” to other voices, Huffman said he doubted any would be persuasive. “I continue to believe a major course correction is needed, and that the President and his team have yet to fully acknowledge the problem, much less correct it,” he said.

But now, several Democrats who requested anonymity were sceptical that there would be enough drive among lawmakers to successfully try to pressure Mr. Biden not to run, especially because they are scattered and away from Washington until next week and because Mr. Biden has said he won’t step aside and seized the opportunity to quickly respond to the shooting over the weekend. The people requested anonymity to characterize private conversations.

Asked by Mr. Holt if he has weathered the worst of it from his own party, Mr. Biden responded that 14 million Democratic voters selected him through the primaries and added, “I listen to them.” His mental acuity is “pretty damn good,” Mr. Biden added, but he said the question of his age was “legitimate” to ask.

Many in the Democratic Party had been looking to congressional leaders Jeffries and Schumer to voice concerns directly to the president. Mr. Jeffries met with Mr. Biden at the White House on July 11 night, while Mr. Schumer went to Rehoboth Beach, Delaware, on July 13 for his visit with Mr. Biden, which occurred just before the assassination attempt on Trump.

There were still deep concerns that Biden is not up to the job and a sense that pressure to try and find another candidate could ramp up again when lawmakers returned to Washington. Congressional Democrats were watching the Republican National Convention and Mr. Biden’s appearances this week with awareness that the dynamics could change — again.