US President-elect Donald Trump has demanded an apology from the cast of the Broadway hit Hamilton for appealing from the stage to Vice President-elect Mike Pence to uphold American values as he sat in the theatre audience.

Mr Trump took time out from his search for appointees to his incoming administration to tweet that Mr Pence "was harassed last night at the theatre by the cast of Hamilton, cameras blazing. This should not happen!"

"The Theatre 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!" Mr Trump tweeted.

Around 11 hours later, Mr Trump tweeted again, saying: "Very rude and insulting of Hamilton cast member to treat our future VP Mike Pence to a theatre lecture. Couldn't even memorize lines!" He later deleted the tweet.

Mr Pence was attending the Friday night performance when star Brandon Victor Dixon, who plays Aaron Burr in the rap musical about America's founding fathers, addressed the audience, saying he hoped the show inspired the incoming vice-president to work on behalf of all Americans.

"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," Dixon said after the performance as Mr Pence left the theatre.

A video of the speech was posted to Hamilton's official social media accounts.

"We truly hope that this show has inspired you to uphold our American values and to work on behalf of all of us," Dixon said, as audience members cheered and clapped.

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Mr Pence was met with a mix of boos and cheers as he entered the Richard Rodgers Theatre in Manhattan before the performance, the New York Times reported.

Videos posted by audience members to social media also showed a mixed response.

Show producer Jeffrey Seller told The Times the election was "painful and crushing" for cast members.

"We are honoured that Mr Pence attended the show, and we had to use this opportunity to express our feelings," said Seller, who helped write Dixon's remarks.

Show creator Lin-Manuel Miranda also posted his support on Twitter.

"Proud of @HamiltonMusical. Proud of @BrandonVDixon, for leading with love," he wrote.

"And proud to remind you that ALL are welcome at the theatre."

The statement came hours after Mr Trump picked three conservative loyalists to lead his national security and law enforcement teams, underscoring his campaign promise to take a hard line confronting Islamist militancy and curbing illegal immigration.

Mr Trump's critics have accused him of racism after he made campaign vows to build a wall on the Mexican border, deport millions of illegal immigrants and scrutinise Muslims for ties to terrorism.

Since his election, the real-estate mogul has called for unity as anti-Trump protests unfolded across the country.

Hamilton is a musical biography of Alexander Hamilton, who rose to become the right-hand man of General George Washington, as well as a key figure in the creation of the US financial system and the creator of the US Coast Guard.

He was killed in an 1804 duel with then vice-president Aaron Burr.

The musical, which won 11 Tony Awards from 16 nominations this year, features a diverse cast and has been hailed as transforming both theatre and the way Americans think about 18th century history, immigration and diversity.

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ABC/Reuters