PITTSBURGH — Just four days into Joe Biden’s presidential bid, the former vice president has quickly sought to define his campaign as a one-on-one battle between him and President Trump, rather than a contest with more than a dozen other Democrats vying for the party’s nomination.

The general-election-style feud escalated further Monday as Biden kicked off his first campaign rally here in Pittsburgh by taunting Trump over labor issues — part of an overt appeal to blue-collar voters that immediately drew Trump’s ire.

Biden’s remarks, in which he accused Trump of ignoring America’s middle-class in favor of the rich, represented a direct challenge to a president whose chances for reelection rest heavily on maintaining support in Rust Belt swing states such as Pennsylvania, Wisconsin and Michigan, all of which Trump won in 2016.

Earlier in the day, Biden picked up an endorsement from the International Association of Fire Fighters, the first major union to offer an endorsement in the campaign. The move drew a retort from Trump, who sought to drive a wedge between union leadership and rank-and-file members.

“I’ll never get the support of Dues Crazy union leadership, those people who rip-off their membership with ridiculously high dues, medical and other expenses while being paid a fortune,” Trump wrote in one of several tweets about Biden. “But the members love Trump.”

Biden posted a tweet a short time later, declaring he was “sick of this President badmouthing unions. Labor built the middle class in this country. . . . We need a President who honors them and their work.”

The exchange marked the latest tit-for-tat as Biden has sought to use his entry into the crowded 2020 Democratic primary race to distinguish his campaign by more directly taking on Trump, while his primary opponents have focused on introducing themselves to voters.

Since officially announcing his candidacy Thursday, Biden has tangled with Trump over the president’s equivocation in denouncing a white supremacists’ march in Charlottesville in 2017 and over which of the septuagenarians has more “vigor” to run the country.

During his remarks at the Teamsters’ hall, Biden addressed workers wearing T-shirts representing the colors of their local union affiliations. A large campaign sign with the slogan “Biden Works for America” hung above the lectern.

“Everybody knows it: The middle class is hurting,” Biden said. “The stock market is roaring, but you do not feel it. There was a $2 trillion tax cut last year, but did you feel it? Did you get anything from it? Of course not. It all went to folks at the top.”

He also accused the president of having “deliberately undermined” the American political system in a bid to “continue to abuse” the office.

“Donald Trump is the only president who has decided not to represent the whole country,” Biden said. “The president has his base. We need a president who works for all Americans.”

For Trump, Biden has offered an irresistible target as the early polling front-runner among Democrats, even as the president has reportedly expressed concerns that the former vice president — who grew up in Scranton, Pa., before settling in Wilmington, Del., for his political career — could present a potent challenge in blue-collar communities.

In other tweets, Trump employed his derogatory nickname for Biden to suggest that the media is “pushing Sleepy Joe hard” to the public. And he said Biden “obviously doesn’t know that Pennsylvania is having one of the best economic years in its history, with lowest unemployment EVER, a now thriving Steel Industry (that was dead) & great future!”

For Biden, Trump’s willingness to engage has helped divert attention from questions from liberal groups over his more conservative positions on criminal justice and immigration while he was a senator and accusations from women who have said they felt uncomfortable by what they perceived as inappropriate touching from Biden. He has said the interactions were part of his emotive political style but promised to be more mindful of personal boundaries going forward.

Biden’s sniping with Trump has also overshadowed recent news stories about Biden’s apparent unwillingness to offer a profuse apology to Anita Hill over her treatment at a 1991 Senate confirmation hearing for Supreme Court Justice Clarence Thomas.

Still, Biden, who chaired that hearing, was asked about it Monday during an interview with “Good Morning America” co-anchor Robin Roberts that will air in full Tuesday on ABC.

“I believed her from the very beginning, but I was chairman,” Biden said. “She did not get a fair hearing. She did not get treated well. That’s my responsibility.”

Biden’s kickoff rally was held near the banks of the Allegheny River, at the banquet hall for the Teamsters Local 249. It was a symbolic choice for a Democrat who has sought to demonstrate he had learned from the mistakes of Hillary Clinton, the 2016 Democratic nominee who lost the Keystone State even though former president Barack Obama won it twice.

“Clinton didn’t win because she didn’t come here,” said Scott Gormley, a 49-year-old Teamster from Pittsburgh who was in the audience. “Our country needs a change. He’s for the middle class, and that’s what we are here.”

During his remarks, Biden called for a $15 minium wage, aligning himself behind a touchstone of the progressive movement, and pledged to reverse the 2017 Republican tax cuts. “We need to reward work in this country,” he said, “not just wealth.”

John Anzalone, a Democratic pollster who advises Biden, said that winning back Trump voters — and convincing primary voters that he is best positioned to do so — is likely to be a major focus of Biden’s strategy. Among many of those voters, Anzalone said, it’s not any one issue as much as it is a sense that he understands them.

“Having a candidate like Biden who speaks their language, who trust him and knows there’s a Democrat who has their back — that’s important stuff,” Anzalone said. “Joe Biden is going to compete with these voters, and that’s what makes him so dangerous to Donald Trump. And Donald Trump knows it.”

Darrin Kelly, the president of the Allegheny County Labor Council, said that Biden was the only Democrat in the position to win the state in the general election against Trump, arguing that other Democrats had moved too far to the left.

Chuck Howenstein, a 63-year-old from Pittsburgh who sells fire equipment, said he switched parties four years ago to become a Republican and voted for Trump in 2016.

“I got caught up in Trump,” he said. But since then, he said, his views have changed because “the division in our country — it’s never been this bad.”

As Howenstein departed Biden’s speech, he vowed to volunteer for him.

“I really do believe he’s a good man,” he said.

Nakamura reported from Washington. David Weigel in Pittsburgh contributed to this report.