MANCHESTER, U.K.—President Trump warned Bruce Springsteen to “keep his mouth shut” until he gets back to the U.S. The rock icon is showing no signs of backing down, delivering a fiery performance from a stage in this city Saturday that reflected the stark political divide in America.

Springsteen echoed earlier criticism of the Trump administration Saturday, saying a “rogue” government was rolling over U.S. lawmakers and institutions designed to keep authoritarianism in check.

“Things are happening right now that are altering the very nature of our country’s democracy,” Springsteen told the audience. To drive the point home, he dedicated one of his songs to our “Dear Leader,” an allusion to the honorific set aside for former North Korean ruler Kim Jong Il.

A similar broadside last week prompted Trump to take aim at Springsteen in a social-media post: “I see that Highly Overrated Bruce Springsteen goes to a Foreign Country to speak badly about the President of the United States. Never liked him, never liked his music, or his Radical Left Politics and, importantly, he’s not a talented guy.”

The escalating confrontation between the president and Springsteen is part of a broader clash between Trump and some pop-culture icons that goes back to the president’s first term. Trump has repeatedly assailed Taylor Swift, who endorsed Kamala Harris in last year’s election but hasn’t engaged in the sort of sharp-tongued criticism delivered by Springsteen.

Trump lashed out at Swift in a separate post Friday: “Has anyone noticed that, since I said ‘I HATE TAYLOR SWIFT,’ she’s no longer ‘HOT?’”

epa10656826 US singer-songwriter Taylor Swift performs during the Eras Tour, at MetLife Stadium in New Rutherford, New Jersey, USA, 26 May 2023. EPA/SARAH YENESEL

Earlier in his administration, Trump trained his fire on some of Washington’s most venerable cultural institutions, complaining that they supported a leftist agenda. In February, Trump made himself the chairman of the board of the John F. Kennedy Center for the Performing Arts and fired board members who had been appointed by Joe Biden and others.

“We didn’t like what they were showing,” Trump said at the time. “We’re going to make sure it’s good and it’s not going to be woke.” Springsteen was honored by the Kennedy Center in 2009, and has performed at Kennedy Center ceremonies for Bob Dylan and Sting during previous administrations.

Some artists have vowed to boycott performances at the center that Trump plans to attend. But few artists have been as blunt as Springsteen, who for decades has cast himself as a champion of the working class and, in recent decades, has regularly campaigned with Democratic Party presidential candidates.

Still, Springsteen has generally been able to straddle the partisan divide in America. His 1984 anthem “Born in the U.S.A.” was widely embraced by Republicans including Ronald Reagan, despite its lyrics’ searing criticism of U.S. foreign and domestic policy. Springsteen also counts former New Jersey Gov. Chris Christie , a Republican and longtime presidential aspirant from Springsteen’s home state, among his biggest fans.

Still, despite Springsteen’s support, the Democratic Party has seen its longtime strength among blue-collar workers eroded by the rise of Trump. The president has transcended his own gilded upbringing to become a hero to many voters across the Rust Belt states that Springsteen has made a career of singing about—including Youngstown, a working-class city in Ohio that was the eponymous subject of one of the songs Springsteen played on Saturday.

Some attendees at Saturday’s concert in Manchester were reluctant to address Springsteen’s politics. Others, like Paul Barnett, 70 years old, a golf-club steward from Knighton, Wales, who has seen Springsteen more than 100 times and described himself as not particularly political, said he was worried about what Trump might do to retaliate against Springsteen when he returns home.

Trump’s latest attacks on Springsteen and Swift drew a response Friday from the American Federation of Musicians, who praised the two artists as “role models and inspirations to millions of people in the United States and around the world.”

During Saturday’s concert in Manchester, Springsteen avoided any direct response to Trump’s latest rhetorical attack, but repeated his critique, including by assailing the president for what he said was his cozying up to foreign dictators and abandoning of longstanding allies. Though the language remained largely unchanged, audience members who attended both Manchester concerts said Springsteen was more impassioned on Saturday.

“He was more on fire,” said Annette Dahlin-Johansson, 56, a Springsteen fan from Gothenburg, Sweden, who attended both concerts in Manchester. The crowd, too, she said, roared back with approval on Saturday in a way that wasn’t the case at last week’s tour opener, when some in the audience appeared surprised by the directness of Springsteen’s political soliloquies.

Many in the crowd Saturday were sympathetic to Springsteen’s political messaging, with several saying it was clear that he was speaking from the heart. One fan-made sign near the stage thanked Springsteen for speaking out, declaring: “I Stand By You.”

Mark Wilcock, a 57-year-old from Skipton, England, who first saw Springsteen in 1988, said Springsteen’s political views have been clear since the mid-1980s, when Springsteen would lead into his cover performances of Edwin Starr’s 1970 hit “War” with a warning against the risks of putting blind faith in political leaders. “It’s still true today,” Wilcock said.

Francis Condron, 55, from Salford, England, said Saturday’s show, his fourth Springsteen concert, was brilliant—especially because he dialed up the politics and attacked Trump. Condron, a former stagehand who now works in a warehouse, said he has long agreed with Springsteen’s politics and called Springsteen’s decision to attack Trump from the stage an act of courage.

Some took specific offense at Trump’s personal put-downs, such as calling the rocker “dumb as a rock” and a “dried out ‘prune’ of a rocker.” Clare Causier, 52, a native of Pontefract, England, offered her own rejoinder for the American president: “He’s an old dried up peach.”

On Saturday, the White House dispensed with Trump’s previous attacks on Springsteen’s intelligence and looks, seeking instead to cast the debate as one between an elected leader and an out-of-touch celebrity.

“The 77 million Americans that elected President Trump disagree with elitist and out-of-touch celebrities like Bruce Springsteen,” said Taylor Rogers, the White House assistant press secretary. “Bruce is welcome to stay overseas while hardworking Americans enjoy a secure border and cooling inflation thanks to President Trump.”

Springsteen’s Manchester shows are the start of his “Land of Hope and Dreams” tour with his E Street Band that will also take him to France, Italy, Germany, the Czech Republic, Spain and Liverpool, England.

Write to Jonathan Cheng at Jonathan.Cheng@wsj.com and Michael R. Gordon at michael.gordon@wsj.com