Donald Trump met Mitt Romney, once a fierce critic of the President-elect who is now being floated as a potential pick for secretary of state, setting aside the friction between the two men and signalling 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 Romney arrived at Trump's New Jersey golf course.

After the meeting, which lasted more than an hour, Romney said the men had had a "very thorough and in-depth discussion" regarding "the various theatres 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: "It went great".

Romney and Trump differ on US relations with Russia. Romney has called the country the "number one geopolitical foe" of the United States. According to the Kremlin, Trump and Russian President Vladimir Putin spoke last Tuesday, agreeing that US-Russian relations are "unsatisfactory" and vowing to work to improve them.

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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". In a speech, Romney called the real estate developer a "con man" and a "fake". Trump said Romney "blew it" and "choked like a dog" in his failed bid to unseat President Barack 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 Vice-President-elect Mike Pence are spending the weekend in a nearly constant stream of meetings with potential administration hires and others looking to dispense advice.

Also yesterday, in a tweetstorm Trump claimed that Pence was "harassed" at a New York theatre where he had gone to see Hamilton, a musical that features a diverse cast. "Our wonderful future VP Mike Pence was harassed last night at the theatre by the cast of Hamilton, cameras blazing. This should not happen!" Trump tweeted.

As Pence entered the theatre, he was met with a chorus of cheers and boos. At the curtain call, the cast stood onstage as actor Brandon Victor Dixon addressed Pence, who apparently was walking out. Some in the crowd started to boo, and Dixon told his audience that there is "nothing to boo here" and urged Pence to hear him out. Later, Trump took to Twitter, saying the cast should apologise. "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. Apologise!" Dixon tweeted: "@realDonaldTrump conversation is not harassment sir. And I appreciate @mike-pence for stopping to listen."

Trump also used Twitter to address a US$25 million settlement to end the fraud cases pending against Trump University. Trump, who had repeatedly claimed that he never settled lawsuits, despite doing so for years, is unlikely now to face the prospect of testifying in court. "I settled the Trump University lawsuit for a small fraction of the potential award because as President I have to focus on our country. 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!"

US Vice-President-elect Mike Pence, top centre, waves as he leaves the Richard Rodgers Theatre after a performance of Hamilton, in New York. Photo / AP
US Vice-President-elect Mike Pence, top centre, waves as he leaves the Richard Rodgers Theatre after a performance of Hamilton, in New York. Photo / AP