President-elect Donald Trump gives a thumbs up as Mitt Romney leaves after a meeting at the Trump National Golf Club in Bedminster, N.J., on Nov. 19. (Jabin Botsford/The Washington Post)

President-elect Donald Trump is for now unswayed by the extraordinarily public revolt by some of his top advisers and allies over the possible choice of Mitt Romney as secretary of state and continues to see his foe as a serious contender for the diplomatic post, several people briefed on the deliberations said Monday.

Romney plans to have a private dinner Tuesday with Trump, who is said to be intrigued by the notion of reconciling with one of his fiercest Republican antagonists — even as he also weighs rewarding the loyalty of former New York mayor Rudolph W. Giuliani with one of the administration’s most prized jobs or selecting a decorated military officer in David H. Petraeus.

Trump is looking for assurances that Romney, the 2012 Republican presidential nominee who has championed a muscular and at times interventionist foreign policy, could be trusted to defend and promote Trump’s markedly different worldview in capitals around the globe, the people familiar with the president-elect’s deliberations said.

Giuliani has openly campaigned for the job and has told friends that he is likely to get it. But Trump’s team has determined that it may be challenging and even unlikely for Giuliani to win Senate confirmation: His web of international business interests and the millions of dollars he has earned in paid speeches and consulting work for foreign entities would come under scrutiny, while Sen. Rand Paul (Ky.), one of 10 Republicans on the Foreign Relations Committee, has threatened to block Giuliani’s nomination.

Romney and Giuliani have been seen as co-favorites to lead the State Department, but Trump this week is expanding his search to include other candidates, chief among them Petraeus, a retired Army general and former CIA director.

Transition officials said Trump has long admired Petraeus and described his candidacy as formidable, despite the baggage he would carry into any confirmation battle because of his 2015 conviction for mishandling classified information. Petraeus’s public service career came to an end amid revelations that he had an affair with his biographer, Paula Broadwell, and shared classified information with her.

On the campaign trail, Trump played down the significance of Petraeus’s conviction, repeatedly arguing that it was “a fraction” of what Democratic nominee Hillary Clinton had gotten away with by using a personal email server as secretary of state.

Petraeus and Trump met Monday afternoon in New York for about an hour, with Vice President-elect Mike Pence joining them for part of the session. As the general exited Trump Tower following their session, he praised Trump, telling reporters that he “showed a great grasp of a variety of the challenges that are out there and some of the opportunities as well. Very good conversation, and we’ll see where it goes from here.”

Trump later tweeted, “Just met with General Petraeus — was very impressed!”

Trump will meet Tuesday with Sen. Bob Corker (R-Tenn.), who officials said could emerge as a candidate, although the senator has said that he is unlikely to end up in serious contention. As chairman of the Senate Foreign Relations Committee, Corker would oversee the confirmation process of Trump’s nominee.

Trump is hiring for other key positions as well, including secretary of homeland security. He met Monday with two candidates: Frances Townsend, a former homeland security official in the George W. Bush administration, and David Clarke, the controversial sheriff of Milwaukee County, Wis. Trump is to meet Tuesday with a third contender, Rep. Michael McCaul (R-Tex.), who chairs the House Homeland Security Committee.

The nascent Trump transition has been riven by infighting over the possible nomination of Romney, who is seen as the quintessential establishment figure and who spoke out against Trump’s candidacy in unusually harsh and personal terms.

Donald Trump's senior adviser and former campaign manager took to the television airwaves on Nov. 27 to lobby publicly against former Massachusetts gov. Mitt Romney as secretary of state. But Trump is set to meet with Romney again on Nov. 29. (Peter Stevenson/The Washington Post)

[The Daily 202: Romney twisting in the wind offers a preview of Trump’s reality-show governing style]

Pence and some Trump advisers are said to have argued that Romney would be a steady hand prepared to help shape relationships around the world. Trump is said to have buried the hatchet with Romney at their Nov. 19 meeting in Bedminster, N.J., and sees a political benefit to bringing him into the administration: silencing a rival Republican who has a big microphone and a network of wealthy donors.

But other Trump intimates have advocated forcefully for Giuliani, a trusted loyalist and brash Trump defender who developed a close bond with the candidate and is more ideologically in sync with him.

The feud spilled into the open over Thanksgiving weekend as Kellyanne Conway, Trump’s former campaign manager and now a senior adviser to the transition team, attacked Romney’s credentials and trustworthiness in a trio of Sunday television appearances. Conway said on CNN that she has received a “breathtaking” amount of messages from Trump supporters “who feel betrayed to think that Governor Romney would get the most prominent Cabinet post after he went so far out of his way to hurt Donald Trump.”

Conway is part of a cadre of Trump allies who are waging an unprecedented public battle against Romney in an attempt to influence the ­president-elect’s decision, sow doubts about Romney in the minds of Trump’s core supporters and create an environment in which he would be a toxic nominee.

Rep. Chris Collins (R-N.Y.), one of Trump’s top backers on Capitol Hill, blasted Romney on Monday on CNN as “a self-serving egomaniac who puts himself first, who has a chip on his shoulder and thinks that he should be president of the United States.”

And Brent Bozell, an influential conservative activist, issued a statement declaring that “the very idea of Mitt Romney as Secretary of State — or any other cabinet position in a Trump administration — is a slap to his supporters.’’

Trump observers said the president-elect has taken a page out of his playbook for “The Apprentice,” his hit reality show on NBC.

“Trump is pitting people against other people, seeing how it plays out,” said Jeffrey Tulis, a professor of government at the University of Texas at Austin. He said Romney is being “humiliated by the process” but that Trump “has a model of conflict between advisers and subordinates that he thinks has worked for him in his business and on his TV show. He’s very comfortable with turmoil.”

[In Trump’s Washington, rival power centers and whispers in the president’s ear]

Over the Thanksgiving break, as Trump relaxed with his wife, Melania, and family at his Mar-a-Lago resort in Palm Beach, Fla., he asked guests and friends to weigh in on the choice between Romney and Giuliani. Two Trump friends confirmed the holiday discussions, which were first reported by the New York Post.

“Donald personally wasn’t negative on Romney, but said he had gotten a lot of negative feedback on Romney, and Melania also had gotten a lot of negative feedback. And it seemed clear he had reservations about Rudy,” said one person close to the transition, who requested anonymity to recount private conversations with the Trumps.

Joe Scarborough, the host of MSNBC’s “Morning Joe,” reported on air Monday that Conway had committed “an act of sabotage” against Romney and that Trump was “furious” with her.

Later Monday morning, on a conference call with reporters, Trump spokesman Jason Miller would neither confirm nor deny that characterization of Trump’s attitude. He said only, “I’ll leave that to the president-elect if he wants to add any additional commentary.”

Miller added that Trump was meeting with Romney on Tuesday because “the two, quite frankly, haven’t spent much time together, so this gives them a little more time to do so.’’

Conway did not respond to a request for comment and declined to speak with reporters at Trump Tower. At 7:37 p.m., she tweeted a photo of her and Trump in his office studying something on a computer screen, saying they were “working hard” together.

One associate said that although Trump “likes the theatrics of it all,” he has chafed at feeling pressured to nominate Giuliani.

Other Trump associates, who also spoke on the condition of anonymity because of the sensitivity of the matter, poured cold water on the suggestion that Conway was freelancing.

“The boss is genuinely conflicted,” one transition official said. A third person, who is close to the transition team, added, “I don’t think Kellyanne went off the reservation. [Still,] Trump would love to have Romney work for him . . . and at the very least, he loves to have Romney grovel for the job.”

Jim Manley, a longtime senior Senate aide who most recently worked for Senate Minority Leader Harry M. Reid (D-Nev.), said the public approach Trump is taking is both “undiplomatic” and “gauche.”

“One of the most important positions in our government is being used as a political football to settle political scores,” Manley said. “Of all my years of watching the confirmation process, I’ve never seen anything like this. . . . You’ve got staff who may or may not be going rogue to advance their own agenda.

“It’s bringing out the worst in people.”

One of Trump’s biggest concerns is whether Romney would advocate Trump’s perspective in closed-door meetings with foreign leaders. The two men have different views on Russia’s aggression and U.S. trade policy, among other issues, although they have similarly aggressive postures when it comes to fighting Islamic State terrorists and cracking down on a Chinese government they see as manipulative and exploitative.

Doug Wilson, chairman of the board of advisers of the Truman National Security Project, said Trump should be certain there is “a cohesive foreign policy that will be supported by all the players.”

“It’s one thing to talk about a team of rivals,” Wilson said, a reference to former president Abraham Lincoln’s Cabinet. “It’s another thing to talk about a team of rivals when you go beyond the water’s edge.”

Still, there is historical precedent for presidents picking secretaries of state from rival wings of their parties: President Obama selected Clinton, while former president Woodrow Wilson tapped William Jennings Bryan.

There also is the question of whether Romney would publicly apologize for his critical statements about Trump during the campaign — something some Trump loyalists are advocating as a condition of his nomination.

One Republican who is close to both Romney and Trump, who spoke on the condition of anonymity, said that for Romney, “The danger is not apologizing. The danger is apologizing and not getting the job.”

David Nakamura in New York and Jerry Markon and Elise Viebeck in Washington contributed to this report.