Retired Army Gen. David H. Petraeus has emerged as a potential secretary of state pick for the upcoming administration of President-elect Donald Trump. (Photo: Anthony Behar/Bloomberg) (Bastien Inzaurralde,Osman Malik/The Washington Post)

President-elect Donald Trump met Monday with retired Army Gen. David Petraeus, a possible alternative choice for secretary of state amid an escalating feud over the position between supporters of former New York mayor Rudolph W. Giuliani and 2012 GOP presidential nominee Mitt Romney, who will sit down with Trump on Tuesday.

As Trump’s senior advisers battled over who should fill what is considered the most prestigious Cabinet post, the president-elect will hold a second session with Romney along with another possible option, Sen. Bob Corker (R-Tenn.), aides said Monday. Corker, who will visit Manhattan’s Trump Tower on Tuesday, chairs the Senate Foreign Relations Committee and had suggested publicly that he was unlikely to be chosen.

But Trump is reportedly considering alternatives for the State Department as an extraordinary feud has broken out between those supporting Romney, a former Massachusetts governor considered the quintessential establishment Republican, and Giuliani, a fierce Trump backer seen by some as deserving the secretary of state post out of sheer loyalty. Romney attacked Trump in unusually harsh and personal terms during the presidential campaign.

The fight hit a fever pitch over Thanksgiving weekend as Kellyanne Conway, Trump’s former campaign manager and now senior adviser to the transition team, took to the airwaves to attack Romney’s credentials to be the nation’s top diplomat. Conway is part of a cadre of Trump confidants who are waging an unusual public battle against Romney to influence the ­president-elect’s decision.

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Another Trump backer, Rep. Chris Collins (R-N.Y.), blasted Romney on CNN’s “New Day” on Monday 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, said in a statement 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.’’

Others inside Trump’s orbit, particularly Vice President-elect Mike Pence, are viewed as Romney supporters, believing that he has a steady hand that would benefit Trump in the turbulent world of diplomacy, according to people familiar with the dispute who spoke on the condition of anonymity to discuss internal deliberations.

Trump was angered at Conway’s remarks, according to a report Monday on MSNBC’s “Morning Joe.’’ Trump aides declined to comment during a conference call with reporters, saying only that the president-elect is taking his time to choose the best possible candidate. Jason Miller, a senior Trump communications adviser, said Trump is meeting with Romney again because “the two, quite frankly, haven’t spent much time together, so this gives them a little more time to do so.’’

The secretary of state search heated up as Trump resumed a busy schedule of transition meetings Monday at Manhattan’s Trump Tower after spending Thanksgiving weekend at his Florida estate. Among those dropping by today will be a candidate for homeland security secretary: Frances Townsend, a top homeland security and counterterrorism official in the George W. Bush administration. Another DHS contender — Rep. Michael McCaul (R-Tex.), chairman of the House Homeland Security Committee — will meet with Trump on Tuesday.

Pence, who will participate in the meetings, entered the Trump Tower lobby Monday morning and paused in front of the elevators amid shouted questions from reporters, saying only: “It’s going to be a busy week. Get ready. Buckle up.”

Trump aides continued Monday to blast a pending recount effort in Wisconsin led by Green Party candidate Jill Stein that has been joined by Democrat Hillary Clinton’s campaign. Trump had spent Sunday ridiculing Clinton’s campaign over the issue, before ending his day on Twitter by parroting a widely debunked conspiracy theory that her campaign benefited from massive voter fraud.

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)

“In addition to winning the Electoral College in a landslide, I won the popular vote if you deduct the millions of people who voted illegally,” Trump tweeted late Sunday, one of more than 10 tweets on the recount issue.

That accusation — spread by conspiracy sites such as ­ and discredited by fact-checking organizations — gained traction among some conservatives disappointed that Trump lost the popular vote to Clinton, though he won the all-important electoral college.

Stein has also filed a recount request in Pennsylvania and plans to do the same in Michigan, her campaign said in a statement Monday. Trump’s surprise victories in the three Great Lakes states was instrumental in his electoral college win.

Miller, in the briefing, added: “I really do think it’s ridiculous that so much oxygen has been given to recount efforts when there is absolutely no chance of the election results changing. This election has been decided. It’s a conceded election.’’

White House spokesman Josh Earnest, who sometimes had harsh words for Trump during the campaign, went out of his way to avoid criticizing the president-elect during his daily briefing Monday. “I think I would defer to the president-elect’s team for commentary on his tweets,” Earnest said.

On the broader election fraud topic, however, Earnest said: “There has been no evidence produced to substantiate a claim like that.’’

Earnest did take issue, however, with Trump’s tweet Monday morning threatening Cuba’s regime in the wake of former president Fidel Castro’s death. Trump vowed to “terminate” President Obama’s efforts to restore full diplomatic relations between the two nations unless Cuba’s communist leaders pursue unspecified changes in their approach.

“If Cuba is unwilling to make a better deal for the Cuban people, the Cuban/American people and the U.S. as a whole, I will terminate deal,” Trump tweeted.

Abandoning the diplomatic reset with Cuba would appease Republican critics of Obama’s efforts, which ran counter to U.S. policy that had aimed to drive Castro from power starting in the 1960s. But Earnest touted what he called the benefits of the policy shift, for both Americans eager to travel to the island nation and for average Cubans.

Summarily reversing Obama’s policy, Earnest said, “is not just as simple as one tweet might make it seem.’’

Petraeus arrived at Trump Tower soon after 2 p.m. Eastern time Monday but did not respond to shouted questions from reporters. Petraeus, who has been taking a “wait and see” approach on joining the new administration, according to a U.S. military official who speaks with him often, has emerged as a possible alternative for secretary of state amid the battle over Romney.

Petraeus returned to the lobby after his meeting with Trump and spoke briefly to reporters.

“I was with him for about an hour,” Petraeus said. “He basically walked us around the world. 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.”

The general is one of the most influential military officers of his generation but ended his government career as director of the CIA in November 2012 amid revelations that he had an affair with his biographer.

Petraeus pleaded guilty in April 2015 to a misdemeanor charge of mishandling classified information in connection with the scandal — namely sharing information with biographer Paula Broadwell — and was sentenced to probation and a $100,000 fine. He could face a tough Senate confirmation process because of that history, though he has since testified before the Senate Armed Services Committee as a foreign policy expert.

Conway over the weekend had led the remarkable rear-guard attack on Romney, arguing that he was disloyal to Trump and should not be considered to run the State Department. The remarks highlighted a fierce behind-the-scenes battle within the Trump camp over whether Romney should be offered the job as a healing gesture with the establishment or whether a loyalist such as Giuliani should get the nod.

Romney’s supporters have largely counseled Trump privately, while his opponents — Conway, former House speaker Newt Gingrich and a handful of other Trump loyalists — have gone public in recent days to stoke a revolt.

Those opposed to Romney have been advocating that Trump reward Giuliani with the secretary of state position, stressing his loyalty vs. Romney’s refusal to publicly say whom he voted for in the presidential race.

“I don’t think a cost of admission for party unity has to be the secretary of state position,” Conway said on ABC’s “This Week,” suggesting that Romney went too far in questioning Trump’s character and intellect during the presidential race. “There was the ‘Never Trump’ movement and then there was Governor Mitt Romney. He went out of his way to hurt Donald Trump.”

The Conway offensive, which began Thursday on Twitter and continued in her three television appearances Sunday, led the echo chamber of opposition to the former 2012 Republican presidential nominee. Gingrich said most Trump supporters could not countenance Romney’s selection for any high-profile posting in Trump’s new administration.

“I think we would be enormously disappointed if he brought Mitt Romney into any position of authority,” Gingrich said on Fox News.

Greg Jaffe, Dan Lamothe, David Nakamura, Philip Rucker and Elise Viebeck contributed to this report.