Donald Trump has heaped praise on the UK’s new prime minister, Boris Johnson, describing him as “Britain Trump” during a speech to hundreds of teenage fans in Washington on Tuesday.

“We have a really good man who’s going to be the prime minister of the UK now,” the US president said. “He’s tough and he’s smart. They’re saying, ‘Britain Trump’. They call him ‘Britain Trump’ and people are saying that’s a good thing.”

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Despite polls and protests to the contrary, he insisted: “They like me over there. That’s what they wanted. That’s what they need. He’ll get it done. Boris is good. He’s gonna do a good job.”

Trump also praised Nigel Farage, the leader of the Brexit party, and looked for him in the audience without success. He said he is confident Johnson and Farage can work together well, he said. Johnson has previously ruled out pacts with Farage.

The president has expressed support for Johnson in recent days, while repeating claims that out former British prime minister Theresa May did not succeed in winning support for her Brexit plan because she ignored his advice on how to handle it.

Trump was speaking to an audience of nearly 1,500 teenagers at Turning Point USA’s Teen Student Action Summit in an upmarket Washington hotel. Before he walked in there were fervent chants of “USA! USA! USA!” and “Trump! Trump! Trump!” from the young conservatives, many of whom wore red “Make America great again” caps. At one point a young woman yelled: “I love you!”

There were cheers when a short biographical film of Trump mentioned his claimed talents in soccer, wrestling, football and baseball, and again for a series of clips in which he said “I like winning” better than merely taking part, insulted comedian Rosie O’Donnell and promised to build a wall.

When footage from the 2016 presidential debates flashed up on the screens, Hillary Clinton was roundly booed. And when a clip quoted Trump saying to her, “Because you’d be in jail,” there were more cheers.

Facebook Twitter Pinterest Young supporters of Trump at the Turning Point USA summit in Washington on Tuesday. Photograph: Nicholas Kamm/AFP/Getty Images

The president delivered a characteristically populist speech that sometimes circled back on itself as it railed against socialism, the “fake news” media, the Russia investigation and political correctness. There was a rousing cheer when he mentioned his daughter, Ivanka Trump, and protecting gun rights.

He went on the offensive against another member of “the Squad” of Democratic congresswomen of color, following his racist attacks last week. Trump insulted Rashida Tlaib of Michigan, who has called for him to be impeached.

He told the audience: “I watched just this morning this Tlaib, Tlaib.” The mere mention of her name generated jeers. “From Michigan, right. That’s a great state. We won Michigan. There’s no way she stands for the values of the people of Michigan.”

In one of his most vicious outbursts yet he lashed out at Tlaib calling her a “not a sane person”.

Play Video 1:07 Donald Trump calls congresswoman Rashida Tlaib a 'crazed lunatic' – video

They like me over there. That’s what they wanted. That’s what they need. Boris is good. He’s gonna do a good job Trump on Johnson

Trump also mocked Alexandria Ocasio-Cortez’s name, saying he will only call her “Cortez” and falsely claimed, “She called our country and our people garbage.” The crowd booed angrily.

Trump has been targeting the women after racist tweets he fired off suggesting they return to their countries, though all are American citizens and all but one was born in the US. At least two members of the audience on Tuesday had signs that said: “Hate US cuz they ain’t US.”

The president said on Tuesday: “I believe they hate our country. We don’t like when they talk about ‘evil Jews.’ We don’t like when they say horrible things about Israel.”

Trump also gloated over how critics had written off his chances in 2016 and mocked Barack Obama for saying he could never win. In response to Obama’s name, someone shouted: “Liar!”

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Trump replied: “He’s right.”

The president repeated claims that Democrats would saddle America with “a socialist nightmare” and false claims their 2020 presidential candidates want to abolish the Department of Homeland Security, meaning that airplanes would no longer be protected. In another obvious falsehood, Trump claimed that undocumented immigrants vote multiple times in California. “They’re rigged.”

Turning Point USA describes itself as a youth organization dedicated to educating and training and students “to promote the principles of freedom, free markets, and limited government”. Trump told its gathering: “There has truly never been a better time to be young and American… There’s greatness in this room. Remember I said it.”