OTTUMWA, Iowa — President Trump and former Vice President Joseph R. Biden Jr. both traveled to the key early voting state of Iowa on Tuesday, trading attacks in sharply personal terms and giving the country a preview of what a general election matchup between the two men might look like.
Mr. Biden, who leads in early polls for the Democratic presidential nomination, described Mr. Trump as “an existential threat” who could fundamentally change the nature of the country and its values, and who is already jeopardizing America’s standing around the world, remarks that came during an afternoon appearance at an events center here.
Mr. Trump, as he departed the Oval Office, told reporters that he thought Mr. Biden was “a loser” and questioned his mental fitness. “I’d rather run against, I think, Biden than anybody,” he said. “I think he’s the weakest mentally, and I like running against people that are weak mentally. I think Joe is the weakest up here. The other ones have much more energy.”
The hostile exchange underscored the extent to which the two men are already waging a battle against one another. Mr. Biden has largely ignored his Democratic rivals while building his campaign around the urgent need to oust Mr. Trump. The president, mindful of polling that shows him trailing Mr. Biden in several key states, has targeted him in particular with ridicule.
While they have attacked each other from a distance, their appearances in the same state on Tuesday seemed primed to intensify the hostility.
Mr. Biden, who began a three-city swing across the state on Tuesday, wasted no time trying to frame the debate, releasing excerpts at 6 a.m. from the remarks he had prepared to deliver at a speech in Davenport in the evening.
The excerpts laced into Mr. Trump over a range of policy issues, such as “pursuing a damaging and erratic trade war” and his approach to tariff negotiations, as farmers — including in this heavily agricultural state — have struggled.
Speaking in Ottumwa, Mr. Biden said that Mr. Trump’s visit to Iowa could be a “clarifying event.”
“Iowa farmers have been crushed by his tariff war with China,” he said.
Mr. Trump, who prides himself on counterpunching, was scheduled to tour an ethanol plant in Council Bluffs in the late afternoon, hours after Mr. Biden’s first event in Ottumwa. Later in the evening, Mr. Trump was set to fly Air Force One across the state, appearing in West Des Moines for a state Republican Party fund-raising dinner as Mr. Biden delivers his speech in Davenport.
Public and private polls that show Mr. Trump trailing Mr. Biden in critical states have also made him most preoccupied with Mr. Biden, whom he has told aides to describe as old and feeble (Mr. Biden is 76; Mr. Trump will turn 73 this week).
Mr. Trump was criticized for attacking the former vice president on foreign soil while visiting Tokyo recently. But his trip to Iowa — a state that twice supported former President Barack Obama before flipping decisively for Mr. Trump in 2016 — will provide him with an appropriate stage on which to take on Mr. Biden.
Up to this point, Mr. Biden has largely resisted responding to Mr. Trump’s individual broadsides, insisting repeatedly that he wants to avoid a “mud-wrestling match” with the president and often ignoring shouted questions from reporters about Mr. Trump’s remarks.
But that hardly means Mr. Biden avoids discussing Mr. Trump. He is centering his campaign squarely on defeating the president, calling him an “aberration.” It’s a point of emphasis sharply at odds with several of his Democratic opponents, who believe Trumpism has redefined the Republican Party and say the country needs bigger, structural change that goes beyond defeating one man.
At every turn, Mr. Biden is seeking to keep the focus on a possible general election matchup between himself and Mr. Trump. He has recently visited Pennsylvania and Ohio, important general election swing states, arguing that he is able to connect in the industrial Midwest and torching Mr. Trump’s leadership approach.
While many of the voters who filed into his Ottumwa event shared Mr. Biden’s near-single-minded focus on Mr. Trump, praising Mr. Biden as someone who could appeal to moderates and independents, Cheri Scherr, 63, said she had hoped to hear “more about his ideas.”
“I wish he would talk less about Trump,” said Ms. Scherr of Pella, Iowa. “We’re Democrats, we know why we don’t like Trump.”
Mr. Biden has generally avoided responding to fellow Democrats, even as his opponents ramp up their critiques of him. One exception came Monday, when he implicitly responded to the entrepreneur Andrew Yang, who had criticized him for missing a gathering of Democrats in Iowa over the weekend that drew most of the primary field.
“My granddaughter was graduating,” he said at a fund-raiser. “It was my daughter’s birthday. I would skip inauguration for that.” He is expected to reiterate a version of that message later on Tuesday.
Mr. Biden has also begun to roll out policy platforms, including on climate and education, though he has released fewer than many of his rivals so far. But on the campaign trail he often underscores that the first step to achieving any Democratic priority is beating Mr. Trump.
“If you want to know what the first, most important plank in my climate proposal is, beat Trump,” he said at his campaign’s first large-scale rally, held last month in Philadelphia. “Beat Trump, beat Trump.”
Mr. Biden’s face-off against Mr. Trump on Tuesday could have downsides, some Democratic strategists cautioned.
“The Biden campaign clearly seems to relish sparring with Trump. In their minds, they believe it elevates him above the rest of the Democratic field,” said Brian Fallon, who served as press secretary for Hillary Clinton’s 2016 campaign. “The potential downside is that as Trump road tests different attacks on Biden, it may help the Democratic primary electorate better visualize potential vulnerabilities that Biden would have in a general election.”
Mr. Fallon said that if any of those attacks — from his supposed lack of energy to his support for the 1994 crime bill — changed voter perceptions, “that could erode the aura of electability that is right now Biden’s strongest asset.”