The president's first-place finish also came as the initial entrance polls from the Democratic caucuses showed a predictably close competition among the party's four top-tier candidates: Joe Biden, Pete Buttigieg, Bernie Sanders and Elizabeth Warren.

Both Walsh and Weld weighed in on Twitter in the minutes after the GOP caucuses were called in Trump's favor.

Walsh shared a message from his campaign manager, who claimed she was receiving reports that "at several precincts across Iowa, including precincts in Urbandale, voters wishing to speak on behalf of Joe Walsh are being turned away/told they may not speak." Those developments, Walsh wrote, were "Very concerning."

Aaron Britt, the communications director for the Republican Party of Iowa, contradicted the Walsh campaign in a statement, saying that the state party "never received reports on anything like that from anywhere."

"Walsh clearly received votes, and the campaign never seemed to be able to identify a specific precinct where there was an issue," Britt said. "Seems like intentional misinformation not backed up by any evidence."

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Weld, meanwhile, posted a photo appearing to show him addressing a crowd of caucus-goers. "The #IowaCaucuses are a great American tradition, and I am honored to participate," he wrote.

The official Twitter account for Trump's campaign was next to comment on its triumph, tweeting that "The Republican Party Has Never Been More United!"

Earlier Monday, various Trump surrogates including the president's sons, senior administration officials and Republican members of Congress had descended upon Iowa to rally support in the hours before the caucuses.