After meeting with President-elect Donald Trump at Trump's golf course in New Jersey, Mitt Romney described it as 'thorough and in-depth discussion' on areas of the world with particular significance to U.S. interests. Trump said the meeting 'went great'. (The Washington Post)

Donald Trump met with Mitt Romney, once a fierce critic of the president-elect who is now being floated as a potential pick for secretary of state, on Saturday afternoon, setting aside the friction between the two men and signaling a willingness by Trump to entertain different points of view on foreign policy.

Romney appeared to warmly shake hands with Trump, each man gripping the arm of the other, as he arrived at Trump’s New Jersey golf course. The two exchanged pleasantries, with Trump placing his hand on Romney’s back, and disappeared behind a large brown door with Vice President-elect Mike Pence.

After the meeting, which lasted for more than an hour, Romney said the men had a “very thorough and in-depth discussion” regarding “the various theaters in the world where there are interests of the United States of real significance.” Romney said that he and Trump exchanged views and that he looks forward to the new administration. Trump said of the meeting: “It went great.”

Romney and Trump hold different views on U.S. relations with Russia. Romney has called the country America’s “number one geopolitical foe.” According to the Kremlin, Trump and Russian President Vladi­mir Putin spoke Monday, agreeing that U.S.-Russian relations are “unsatisfactory” and vowing to work together to improve them. Trump’s office said in a statement that the president-elect told Putin he was looking forward to “having a strong and enduring relationship with Russia and the People of Russia.”

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The cordiality that Romney and Trump displayed publicly was a marked change from the way the men spoke about each other during the campaign.

Romney told CNN in June that a Trump presidency could bring “trickle-down racism, trickle-down bigotry, trickle-down misogyny” to the nation. In a speech, Romney called the real estate mogul a “con man” and a “fake.” Trump said Romney “blew it” and “choked like a dog” in his failed bid to unseat President Obama in 2012, and he called the former Massachusetts governor “one of the dumbest and worst candidates in the history of Republican politics.”

Trump and Pence are spending the weekend at Trump National Golf Club in Bedminster, N.J., in a nearly constant stream of meetings with potential administration hires and others looking to dispense advice. Trump said Saturday evening that he was seeing “tremendous talent.” When asked if his cabinet was being shaped, he said: “Yes. Partially. We’re doing this again tomorrow.”

He and Pence met earlier in the day with retired Marine Gen. James Mattis, a potential pick for secretary of defense who could be seen as a rebuke to President Obama. Mattis oversaw U.S. forces in the Middle East from 2010 to 2013. He was said to have consistently pushed the military to punish Iran and its allies, including calling for more covert actions to capture and kill Iranian operatives and interdictions of Iranian warships.

Former defense officials said Mattis’s views on Iran caused him to fall out of favor with the Obama administration, which was negotiating the Iranian nuclear deal at the time. Mattis, who also clashed with the administration over its response to the Arab Spring and how many troops to keep in Iraq, was forced to retire earlier than expected to clear room for his replacement at U.S. Central Command. Now a fellow at Stanford University’s Hoover Institution, Mattis has publicly criticized Obama’s defense and national security policies.

When asked whether he would choose Mattis as defense secretary, Trump said: “We’ll see.” He called the retired general “the real deal” and a “brilliant wonderful man.” A source familiar with transition discussions, speaking on condition of anonymity, said that no decision has yet been reached about whether Mattis will join the Trump administration.

Michelle Rhee, the former D.C. schools chief who is being floated as a possible education secretary, and her husband, Sacramento Mayor Kevin Johnson, also met with Trump and Pence. Rhee served three contentious years as chancellor of the District’s schools, where she oversaw a rise in test scores but shuttered some schools, laid off nearly 700 teachers for poor performance and filled more than 91 principal openings that were created via firings, resignations and retirements. Rhee has been a supporter of Common Core, which Trump opposes.

Trump also met with donor Betsy DeVos, who is also reportedly being considered for education secretary. DeVos is a proponent of charter schools and vouchers.

Patrick Soon-Shiong, a billionaire oncologist who advised Vice President Biden’s efforts to combat cancer, also met with Trump and Pence on Saturday afternoon, as did conservative community development leader Robert L. Woodson Sr., who told The Washington Post that he is under consideration to be secretary of housing and urban development.

The president-elect and vice president-elect are also planning to huddle this weekend with Kansas Secretary of State Kris Kobach, an immigration hard-liner who is on Trump’s transition team, and New Jersey Gov. Chris Christie, who was ousted as chairman of Trump’s transition team.

“These meetings that the president-elect and vice president-elect are having really show . . . the depth to which we’re going to pull in diverse ideas and different perspectives as we form this administration,” Trump spokesman Jason Miller said Saturday.

Some visitors, he said, are “potential administration hires,” while others are coming only to offer advice. “The president-elect is bringing together folks who have been on the opposite side of him politically,” Miller said.

Questions about Trump’s ability to bring Americans together arose onstage Friday night on Broadway.

In a morning tweetstorm — a communication method that Trump often used as a candidate but that is unprecedented for a president-elect — Trump claimed that Pence was “harassed” Friday night at a New York theater, where he went to see “Hamilton,” a Tony Award-winning musical about Founding Father Alexander Hamilton that features a diverse cast and crew.

“Our wonderful future V.P. Mike Pence was harassed last night at the theater by the cast of Hamilton, cameras blazing. This should not happen!” Trump tweeted.

At the show’s curtain call, the cast stood onstage as actor Brandon Victor Dixon, who portrays Hamilton nemesis Aaron Burr, addressed Pence, who apparently was walking out of the theater.

“We sir, we are the diverse America who are alarmed and anxious that your new administration will not protect us, our planet, our children, our parents, or defend us and uphold our inalienable rights, sir,” Dixon said during his remarks. “But we truly hope that this show has inspired you to uphold our American values and to work on behalf of all of us — all of us.”

A spokesman for the show told the Associated Press that Pence stood outside the theater to listen to Dixon.

Later, Trump took to Twitter, saying the cast should apologize for addressing Pence.

“The Theater must always be a safe and special place. The cast of Hamilton was very rude last night to a very good man, Mike Pence. Apologize!”

Dixon tweeted back to Trump: “@realDonaldTrump conversation is not harassment sir. And I appreciate @mike_pence for stopping to listen.”

Trump also used Twitter to address a $25 million settlement to end the fraud cases pending against Trump University, a defunct real estate seminar program. Trump, who had repeatedly claimed that he never settled lawsuits, despite doing so for years, now will likely not face the prospect of testifying in court during his presidential transition.

“I settled the Trump University lawsuit for a small fraction of the potential award because as President I have to focus on our country,” Trump tweeted.

He added: “The ONLY bad thing about winning the Presidency is that I did not have the time to go through a long but winning trial on Trump U. Too bad!”

New York Attorney General Eric Schneiderman said Friday that the settlement includes a $1 million penalty paid to the state for claiming the program was a “university” even though it did not offer degrees, violating New York education law.

Emma Brown, Greg Jaffe, Missy Ryan and Amy B Wang contributed to this report.