Biden, a Democratic former senator from Delaware who served for eight years as President Barack Obama’s No. 2, officially launched his bid for the 2020 Democratic nomination Thursday with an explicit rejection of Trump and his values, focusing in particular on the president’s declaration that there were “very fine people on both sides” of deadly clashes between white supremacists and counterprotesters in Charlottesville in 2017.

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Trump immediately responded by insulting Biden’s intelligence on Twitter and branding him “Sleepy Joe.” If Biden can prevail over the gantlet of nearly two dozen Democratic hopefuls, Trump wrote, “I will see you at the Starting Gate!”

But by Friday, the two were already out of the gate, engaged in an early round of bickering in which the 72-year-old president and the 76-year-old former vice president seemed determined to establish who was more energetic and virile.

Leaving the White House on Friday morning, Trump enthused to reporters about how he is “the youngest person.”

“I am a young, vibrant man,” Trump said, apparently drawing a contrast with Biden.

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When asked on ABC’s “The View” about Trump calling him “Sleepy Joe,” Biden smiled.

“That’s the first time I’ve ever been referenced that way,” he said. Usually, Biden added, it’s the other way around: “Hyper Joe.”

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The contest of machismo between the two generational peers — another candidate seeking the Democratic nomination, Sen. Bernie Sanders (I-Vt.), is 77 — has prompted some amusement among political spectators. “I’m not sure ‘Grumpy Old Men 3’ is the debate America wants or needs right now,” said Michael Steel, a Republican strategist.

But for Trump, his nicknames and digs at Biden belie a deeper worry: For now, at least, Trump and those in his orbit largely view Biden as his most potent rival, according to people familiar with Trump and his team’s thinking.

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An adviser who recently spoke to Trump about the campaign said he was focused on Biden and Sanders, asking about their rollouts and popularity and which candidate would be a more formidable foe. Biden poses a particular threat, some campaign advisers say, in places such as Wisconsin, Michigan and Pennsylvania — states that Trump won in 2016 with strong support among working-class whites.

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A second adviser said part of Trump’s current interest in Biden is simply because the Democratic challenger is dominating cable news that the president consumes and leading in polls that the president watches closely. On Friday afternoon, the Biden campaign further established its early dominance by announcing that he had raised $6.3 million in his first 24 hours as a candidate — a figure that bests the first-day hauls of other Democrats.

Others in Trump’s orbit, however, say that while Biden may be the candidate du jour, they are skeptical of his staying power.

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“I don’t see how Biden is going to be able to survive the onslaught that’s coming from both the left and the right,” said Andy Surabian, a Republican strategist and former Trump White House official. “Because he’s not only leading the Democratic primary, but he’s also currently seen by most observers as the strongest opponent in a general election, Republicans are going to be launching as many arrows at him as his primary opponents are, and that’s the key thing — the attacks are going to be coming from all angles.”

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The Trump campaign, for its part, is still hoping to focus on the Democrats more generally, painting them in broad strokes as socialists. Campaign communications director Tim Murtaugh said the goal is for the eventual Democratic nominee to be “saddled with all the socialist policies they will have adopted in order to win the nomination.”

“There is no centrist lane in the Democrat primary, and Joe Biden admitted as much when he said he had the most ‘progressive’ record of anybody in the field and claimed he had never been labeled a moderate in Delaware,” Murtaugh said in an emailed statement.

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Biden’s announcement video began with a discussion of Charlottesville and Trump’s “both sides” statement.

“With those words, the president of the United States assigned a moral equivalence between those spreading hate and those with the courage to stand against it,” Biden said, staring directly into the camera. “And in that moment, I knew the threat to this nation was unlike any I had ever seen in my lifetime.”

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The focus on Trump’s response to Charlottesville — one of the more-controversial moments in a presidency full of them — forced Trump on the defensive. On Friday, the president said he was simply referring to the people who were at the rally protesting the removal of a monument to Robert E. Lee, who, he added, “was one of the great generals.”

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Biden’s campaign aides say they welcome the fight with Trump as a way to draw a general-election contrast. One of the main thrusts of Biden’s campaign is the argument that he is best positioned to counter Trump by winning over voters in the industrial Midwest who Trump carried in 2016, and advisers cite public and private polling that shows Biden has more standing than any other Democrat.

But they are also eager to showcase the former vice president’s ability to go toe-to-toe with Trump on issues both substantive and petty in a way that most Democrats have struggled to do.

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“If he looks young and vibrant compared to me, I should probably go home,” Biden said during his appearance on “The View.” “Everybody knows who Donald Trump is. The best way to judge me is watch. See if I have the energy and capacity. This is a show-me business.”

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For all the differences the two candidates are eager to highlight between them, similarities abound. Both are old-school male politicians who have long had access to the corridors of power — politics for Biden, finance and entertainment for Trump — but still view themselves as outsiders. Biden grew up in a working-class Irish Catholic family, and Trump still sees himself as the outer-

borough Queens kid who could never gain the acceptance of Manhattan elites.

They have also both embraced a reputation for authenticity, parlaying into an asset what for other politicians might be a liability leading to frequent gaffes.

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Biden, again and again, has also demonstrated a Trump-like refusal to apologize. On Friday, that resistance was on display as he declined to apologize for pretty much anything during his interview on “The View.”

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When asked about his interactions with women who said they felt uncomfortable when he hugged them, pressed his forehead against theirs, rubbed noses with them or sniffed their hair, he said he had learned a lesson but that he wasn’t exactly sorry.

“So I invaded your space,” Biden said. “I’m sorry this happened. But — but I’m not sorry in the sense that I think I did anything that was intentionally designed to do anything wrong or be inappropriate.”

Trump, meanwhile, seemed determined to taunt Biden, as well as any other potential 2020 Democratic threats.

“I would never say anyone is too old,” the president said Friday morning, before doing exactly that. “But I know they’re all making me look very young, both in terms of age and, I think, in terms of energy.”