Gov. Ron DeSantis of Florida said on Friday that he expected Donald J. Trump to claim that the Iowa caucuses had been “stolen” if the former president, who currently leads Mr. DeSantis by roughly 30 points in that state, is defeated there next month.

“If Trump loses, he will say it’s stolen no matter what, absolutely,” Mr. DeSantis said, responding to a reporter in New Hampshire who had asked whether Mr. Trump would accept the results of the first contest in the Republican presidential primary on Jan. 15, or of the New Hampshire primary roughly a week later. “He will try to delegitimize the results. He did that against Ted Cruz in 2016.”

Mr. DeSantis added that Mr. Trump had protested “even when ‘The Apprentice’ didn’t get an Emmy,” referring to the former president’s onetime television show.

Throughout the 2024 campaign, Mr. Trump and his allies have continued to insist that he defeated President Biden in 2020. The constant chorus of falsehoods seems to have seeped into the consciousness of many Republicans. Nearly 60 percent of G.O.P. voters believe Mr. Biden’s election was illegitimate, a survey by The Associated Press found earlier this year.