“The president is literally an existential threat to America,” Biden said in Ottumwa, the first of several events in Iowa in which he delivered a multipronged indictment of Trump’s policies, values and character.

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Trump, who has repeatedly brushed aside the advice of aides who warn against elevating Biden by attacking him, responded with the plain-spoken vitriol that built his political brand. He pointed to Biden’s dismal finish in the 2008 presidential campaign, saying Barack Obama “took him off the trash heap” by making Biden his running mate, and suggesting the former vice president has lost a step.

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“He’s a different guy,” Trump said as he left the White House for Iowa. “He looks different than he used to. He acts different than he used to. He’s even slower than he used to be.” Biden is 76 and Trump will be 73 on Friday, making both significantly older than most of the Democratic field.

“Joe Biden is a dummy,” Trump concluded.

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Unlike his rivals, Biden from the outset has focused his campaign on Trump’s suitability for office, launching his effort in April with a video showing the white supremacist march in Charlottesville and Trump’s response to it, which Biden portrayed as weak and even immoral.

Tuesday was essentially a day when both Biden and Trump got the campaign they wanted. In the state that holds the first presidential nominating votes, Biden was able to frame the race as a contest between himself and the president, with the other 22 Democratic hopefuls largely crowded out of the picture. And Trump could focus his fire, and his insults, on a single rival, in a campaign that otherwise has featured a diffuse and shifting Democratic field.

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Biden’s focus on Trump came after a difficult few days for his presidential run. His campaign admitted to plagiarizing a policy document, and Biden — after initially holding to his decades-long support for a rule against federal money being used for abortions — was forced to abruptly reverse himself amid an outcry led by Democratic women.

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At the same time, a poll in the Des Moines Register showed that Biden was leading the Democratic field in Iowa but that other candidates — including Sen. Elizabeth Warren (Mass.) and South Bend, Ind., Mayor Pete Buttigieg — were gaining strength, with supporters who were more passionate about them.

Beyond that, several of the other candidates have begun attacking Biden more directly, after an initial stretch in which they’d been more cautious. Sen. Bernie Sanders (I-Vt.) has taken a particularly forceful tone against what he sees as Biden’s middle-of-the-road policies.

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The Trump-Biden show dominated most of the day on Tuesday, with clash-of-the-titans news coverage and Biden receiving the kind of wall-to-wall cable television presence that other Democratic candidates have craved and rarely gotten. The three major cable networks — including Fox News, which can be less prone to cover Democratic events — presented a large dose of Biden’s first Iowa event.

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The one-on-one exchange, though, carries risk for both men. Some Democrats note that the party won last year’s midterm congressional elections by focusing tightly on issues like health care and jobs, rather than talking about the president and his character. Trump can be a political tornado, sucking in his opponents in and forcing them into a debate on his terms, which can easily turn personal and destructive.

Trump, meanwhile, has arguably benefited from an opposition that’s divided among 23 widely divergent candidates and a Democratic Party that could face a long, bitter slog to settle on a nominee. By quickly elevating one candidate as an opponent worthy of attack, Trump could reduce that advantage.

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Responding to Biden’s volleys, Trump on the South Lawn of the White House called the former vice president a “loser,” “dumb” and “mentally weak.”

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“I’d rather run against, I think, Biden than anybody,” Trump said. “I think he’s the weakest mentally. The others have much more energy.”

Biden has said that he doesn’t want to get in a “mud-wrestling match” with Trump, but Tuesday’s remarks made it clear he was prepared to get a little dirty.

The devastating flooding that has damaged Iowa and other parts of the Midwest, Biden said, illustrated the impacts of Trump’s skepticism of climate change (“It’d be funny if it wasn’t so, so damaging”). The president’s attempts to repeal the Affordable Care Act, he argued, pose a risk to Americans who are now covered.

Trump, he said, was not only destroying American alliances but also he was petty and unfocused while doing so. “He found time to go after Bette Midler, for God sakes — in the middle of the D-Day ceremonies,” Biden said.

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Biden released his prepared remarks for a stop in Davenport — all 2,887 words of them — at 6 a.m. Tuesday, getting a jump on the day and guiding cable news coverage in a way that Trump often does in 280-character increments on Twitter.

Those remarks asserted, among other things, that Trump’s escalation of tariffs between the United States and China has “crushed” farmers in Iowa. “He thinks he’s being tough,” Biden said. “Well, it’s easy to be tough when someone else is feeling the pain.”

Trump disputed that he was hurting farmers, citing bailouts his administration has offered to farmers hurt by his trade war.

“Nobody has treated the farmers better than Donald Trump,” the president said, adding that he expects to win Iowa “very easily” next year.

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Biden also sought to address a comment he made recently about China that drew criticism from Trump. Last month, he said China is “not competition for us” geopolitically, prompting Trump to call him “very naive.”

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Biden said Tuesday he does consider the country a significant threat, adding in his prepared remarks that he is “worried about China — if we keep following Trump’s path.”

In speaking to reporters in Mount Pleasant, Iowa, Biden took a defensive tone, downplaying the need for debate preparations (“This is going to be an appearance, less than a debate”), the sentiments of voters wanting a fresh face (“Vote for a new person then”), and insisting that he was overshooting media expectations for his campaign (“You all said I was going to fail from the beginning. You said it!”).

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He also launched into an extended argument that while politics needs more civility, the overall system of government does not.

“They said that we’ve got to have a new system. The same people that say: ‘We’ve got to have somebody totally new. We’ve got to change the system,’” he said. “Well guess what? Systems work pretty damn well. It’s called the Constitution. It says you have to get a consensus to get anything done.”

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Trump has taken aim at some of the other Democratic presidential candidates, calling Warren “Pocahontas” because of her claims of Native American heritage, dismissing Buttigieg as “Alfred E. Neuman,” the gaptoothed Mad magazine mascot, and dubbing Sanders “Crazy Bernie.”

But he’s signaled he views Biden as the most likely nominee, and especially after Tuesday seems to be directing most of his fire at the former vice president, who was part of an Obama administration that Trump often criticizes.

After flying on Air Force One, with the televisions tuned to Biden’s speech carried on Fox News, Trump appeared in western Iowa at an ethanol plant in Council Bluffs, where he interspersed more Biden criticisms in remarks on the economy, calling him “sleepy.”

All day, both Trump and Biden seemed obsessed with how much the other was obsessed with him. “He said my name so many times that people couldn’t stand it anymore,” Trump said of Biden.

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“I guess he’s really fascinated with me. I find it fascinating,” Biden said of Trump.

Trump and Biden appeared on opposite ends of the state, making their convergence more symbolic than literal. It came three days after much of the rest of the Democratic field appeared in Iowa for a state party event.

Biden skipped the event — citing his daughter’s birthday and his granddaughter’s high school graduation — and was criticized by some of his rivals, who have visited Iowa more often and have been attending candidate forums that Biden has avoided.

As he arrived on Tuesday, Biden focused his attention on some of the areas that swung from Obama to Trump in 2016. His first event in Ottumwa was in rural southeastern Iowa, about 85 miles south of Des Moines. The county voted twice for Barack Obama — who won about 55 percent of votes in both 2008 and 2012 — and then Trump won the county in 2016 with 57 percent of votes. The swing was one of the largest in a state where nearly a third of counties flipped from Obama to Trump.

Among those in the crowd waiting for Biden in Ottumwa was Patti Durflinger, 61, from nearby Eldon — a historically Democratic town that went for Trump in 2016.

It didn’t bother her, she said, that Biden didn’t show up for the candidate forum in Cedar Rapids or that he’s had a lighter schedule than some of his Democratic opponents in the state.

But Durflinger said Biden “needs to bring energy” to the race, and he can only do so by campaigning more and “bringing the fight to Trump.”

“He’s got to get people riled up, too — he’s got to get people riled up like Trump did,” Durflinger said. “We need the Democrats to come out. And I think he can be the man to do that. He just has to be here, show up.”