DES MOINES, Iowa — President Trump scored a record-setting win in the Iowa caucuses on Monday with his rivals languishing far behind, a victory that affirmed his grip on the 2024 Republican presidential nomination.

In what was the lowest-turnout caucus in a quarter-century, participants endured life-threatening cold and dangerous driving conditions to meet in hundreds of schools, churches and community centers across the state. 

Yet those who ventured out delivered a roughly 30-point win for Trump that smashed the record for a contested Iowa Republican caucus with a margin of victory exceeding Senator Dole’s nearly 13-percentage-point victory in 1988.

Governor DeSantis finished a distant second, just ahead of the former American ambassador to the United Nations, Nikki Haley. Biotech entrepreneur Vivek Ramaswamy finished a distant fourth, prompting him to suspend his bid for the nomination and endorse Mr. Trump.

The results left Mr. Trump with a tighter grip on the GOP nomination, though it could take several more months for anyone to formally become the party’s standard bearer. 

The magnitude of Mr. Trump’s victory, however, posed significant questions for both DeSantis and Haley. Neither candidate appeared poised to exit the race, though they leave Iowa struggling to claim making much progress in trying to become Trump’s strongest challenger.

Mr. Ramaswamy said he made the decision to quit the race after determining there was no path forward for him, “absent things that we don’t want to see happen in this country.”

The 38-year-old political novice, who sought to replicate Mr. Trump’s rise as a bombastic, wealthy outsider, said he called the former president earlier Monday evening to congratulate him. 

Mr. Ramaswamy told supporters gathered at a Des Moines hotel that Mr. Trump “will have my full endorsement for the presidency.”

Mr. Trump, in his victory speech a few minutes earlier, said Ramaswamy “did a helluva job” in the campaign.

Having repeatedly vowed vengeance against his political opponents in recent months, Mr. Trump offered a message of unity in his victory speech.

“We want to come together, whether it’s Republican or Democrat or liberal or conservative,” he said. “We’re going to come together. It’s going to happen soon.”

The GOP contest moves swiftly to New Hampshire, where the shrinking field will hold the first-in-the-nation primary on January 23. 

Mr. DeSantis first heads to South Carolina on Tuesday, a conservative stronghold where the February 24 contest could prove pivotal. He will head later in the day to New Hampshire.

“Because of your support, in spite of all of what they threw at us, we got our ticket punched out of Iowa,” Mr. DeSantis told supporters.

Mrs. Haley plans to compete vigorously in New Hampshire, where she hopes to be more successful with the state’s independent voters.

“When you look at how well we’re doing in New Hampshire and in South Carolina and beyond, I can safely say tonight Iowa made this Republican primary a two-person race,” she said.

In a preview of a remarkable balancing act Mr. Trump may have to manage in the months ahead, he was expected to be in court in New York on Tuesday. 

A jury is poised to consider whether he should pay additional damages to a columnist who last year won a $5 million jury award against Mr. Trump for sex abuse and defamation. It’s just one of multiple legal challenges facing the former president.

After visiting the court, Mr. Trump will fly to New Hampshire to hold a rally Tuesday evening.

Mr. Trump has made courtroom visits a part of his campaign — heading to court voluntarily twice last week while his opponents campaigned in Iowa — in a strategy designed to portray him as a victim of a politicized legal system. Among Republican voters, at least, the approach is working.

The Associated Press declared Mr. Trump the winner of the Iowa caucuses at 7:31 p.m. CST based on an analysis of early returns as well as results of AP VoteCast, of more than 1,500 voters who said they planned to take part in the caucuses. Both showed Mr. Trump with an insurmountable lead.

Iowa has been an uneven predictor of who will ultimately lead Republicans into the general election. President George W. Bush’s 2000 victory was the last time a Republican candidate won in Iowa and went on to become the party’s nominee.