Some break bread to put the past behind them. President-elect Donald Trump and Mitt Romney dined on frog legs.

The lavish dinner at a French restaurant in a Trump hotel in Manhattan on Tuesday marked the latest chapter in Mr. Romney’s transition from a fierce critic of the president-elect during the Republican primary to a top contender for secretary of State. While the courtship hasn’t been well received by some members of Mr. Trump’s transition team, Trump would be following the example set by the Obama administration if he were to put aside campaign rivalries and choose Romney as secretary of State.

Following the dinner, Romney, the former Massachusetts governor and 2012 Republican presidential nominee, all but apologized in efforts to make amends with Trump and move forward.

He praised Trump for a “message of inclusion and bringing people together” since he won the general presidential election on Nov. 8.

Romney also referenced the cabinet positions Trump has filled for his administration, and said the president-elect desires greater unity among Americans.

“All of those things combined give me increasing hope that President-elect Trump is the very man who can lead us” to a better future, he said.

The former governor's tone is notably different than his sharp criticism of Trump during the campaign. In a March speech in Utah, Romney said Trump posed a fundamental threat to American democracy, as The Wall Street Journal reported.

“If we, Republicans, choose Donald Trump as our nominee, the prospects for a safe and prosperous future are greatly diminished,” he said at the time. “Donald Trump is a phony, a fraud. His promises are as worthless as a degree from Trump University. He’s playing the members of the American public for suckers: He gets a free ride to the White House, and all we get is a lousy hat,” he added.

But after Trump’s victory, Romney and Vice President-elect Mike Pence met to settle their differences. Following a Nov. 19 meeting at Trump National Golf Club in Bedminster, N.J., Romney said he and Trump had a “far-reaching conversation.” Since then, Romney’s name has emerged alongside that of former New York Mayor Rudy Giuliani, a longtime friend and Trump loyalist, as the main contenders for the top cabinet post. Trump is also considering retired Marine Corps Gen. John Kelly and Sen. Bob Corker (R) of Tennessee for the post.

Reince Priebus, the Republican National Committee chairman whom Trump named his chief of staff, has been pushing for Romney to become secretary of State, a Republican source close to the transition effort told Reuters. Mr. Priebus joined Trump and Romney for the lengthy dinner on Tuesday, which included garlic soup with frog legs, scallops, steak, and lamb chop.

But Romney’s name on this short list hasn’t resonated with other members of Trump’s transition team. Former house speaker Newt Gingrich, who has openly supported Mr. Giuliani, former Arkansas Gov. Mike Huckabee, and Kellyanne Conway, a senior adviser to Trump, have all publicly raised their objections to the idea of Romney as secretary of State.

“People feel betrayed to think that Governor Romney, who went out of his way to question the character and the intellect and the integrity of Donald Trump, now our president-elect, would be given the most significant Cabinet post of all, secretary of State,” Ms. Conway told NBC’s “Meet the Press” on Sunday, as she slammed Romney on the morning political-show circuit. “They feel a bit betrayed to think that you can get a Romney back in there after everything he did.”

Trump has already nominated other critics to key cabinet positions. He named South Carolina Gov. Nikki Haley as ambassador to the United Nations. Ms. Haley, the daughter of Sikh immigrants, clashed with Trump over his comments about Mexicans and Muslims and endorsed Sens. Marco Rubio (R) of Florida and Ted Cruz (R) of Texas during the Republican primary. Trump also named Betsy DeVos as secretary of Education. Ms. DeVos was a delegate for Ohio Gov. John Kasich at the Republican National Convention. Both cabinet positions require Senate confirmation.

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Even though Trump has been said to value loyalty, his consideration of Romney and other critics isn’t unusual. President Obama was credited with bringing together a “team of rivals” for his administration. Vice President Joe Biden and former Secretary of State Hillary Clinton had both run against Mr. Obama during the 2008 Democratic primary.

This report contains material from the Associated Press and Reuters.