Donald Trump is projected to win Iowa's caucuses, the first of the state-by-state contests where Republican voters will pick their White House candidate.
Florida Governor Ron DeSantis was projected to win a distant second place, with Nikki Haley in third.
Mr Trump won strong support from white evangelicals and very conservative voters, say entrance poll data.
The eventual Republican nominee will challenge the Democrat pick, probably President Joe Biden, in November.
In remarks in the state capital Des Moines, Mr Trump praised his closest rivals saying "they both actually did very well" and turned his aim on Mr Biden.
"So I don't want to be overly rough on the president," he said. "But I have to say that he is the worst president that we've had in the history of our country."
A pro-Trump political action committee called on his rivals to pull out to avoid a protracted battle and save resources for the general election.
A senior official for the DeSantis campaign said: "They threw everything at Ron DeSantis. They couldn't kill him. He is not only still standing, but he's now earned his ticket out of Iowa."
Biotech entrepreneur Vivek Ramaswamy, meanwhile, announced he was suspending his presidential campaign after he seemed on course for a distant fourth-place finish in Iowa. He endorsed Mr Trump.
Registered Republicans braved sub-zero temperatures to gather on Monday evening across Iowa to cast ballots at churches, schools, gyms, and community centers.
At a high school in Davenport, in the eastern part of the state, Trump supporter Brian Romer gave an impassioned speech to his fellow Republicans in favor of the former president.
"The things that happen in this country are things that happen in communist countries," he said, referring to Mr Trump's criminal indictments. "We don't live in a free country anymore."
According to the entrance poll data, Mr Trump won men, women, older voters, and younger voters, improving on his 2016 performance with all of these groups.
Most Iowa caucus-goers largely dismissed his ongoing legal woes, saying he would still be fit for the presidency even if he were convicted of a crime.
The issue of immigration helped boost Mr Trump: he overwhelmingly won those who picked this as their top issue.
Most Republican voters in Iowa said they favoured a nationwide ban on all or most abortions, and most of those voters also went for Mr Trump.
But other Republicans including Mike Johnson, Speaker of the US House of Representatives, congratulated Mr Trump.
"Tonight's vote was an endorsement of President Trump's extraordinary record and his ongoing vision to fix our economy, secure our border, and defend the freedoms and values that make America great," the Louisiana congressman said.
Mr Trump, the runaway frontrunner nationally in the Republican race, had been the overwhelming favourite to win Iowa.
Ms Haley, aiming to be the first female US president, has enjoyed a boost in support in the wake of headline-making debate performances.
Source: BBC News
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