Mr. Trump and Mitt Romney — who called Mr. Trump a “phony” and a “fraud” during the Republican primaries — sat down for a four-course meal Tuesday night at Jean-Georges, a three-star Michelin restaurant at the Trump International Hotel and Tower in Manhattan.

Mr. Romney, the former Massachusetts governor, emerged several hours later to heap compliments on the president-elect, who has bristled privately that Mr. Romney never apologized for insulting him during the race.

On Tuesday, there was no apology, but Mr. Romney said he had been impressed by Mr. Trump’s victory speech on election night, his transition effort, and his personnel decisions.

“He did something I tried to do and was unsuccessful in accomplishing: He won the general election,” Mr. Romney told reporters. “He continues with a message of inclusion and bringing people together, and his vision is something which obviously connected with the American people in a very powerful way.”

He said Mr. Trump’s conduct since winning the election gives him “increasing hope that President-elect Trump is the very man who can lead us to that better future.”

Mr. Romney is said to be under consideration for secretary of state.