The interview comes just days after Trump refused to back Mrs May after her government was plunged into crisis over the shock resignations of Johnson and former Brexit secretary David Davis.
Trump came down firmly on the side of the Brexiteers, saying what May proposed would hurt the chances of a future trade deal between the UK and the United States.
But 51% again say that the U.S. president is untrustworthy to negotiate a trade deal with, including 38% who say he is "very untrustworthy".
Trump's interview with the paper came after his contentious meeting with North Atlantic Treaty Organisation members in Brussels and ahead of his scheduled visit with Queen Elizabeth II. This is what White House spokespeople do when a statement they're tasked to deliver is ridiculous and they'd rather attribute it to Trump rather than sacrifice their own credibility.
"This incredible woman right here is doing a fantastic job, a great job", he said.
He added: "I would have done it much differently". He also said a rival politician, Boris Johnson, would make a "great prime minister". At issue is an interview in the tabloid Sun newspaper in which he was critical of May on Brexit and for not taking his advice (otherwise she'd be better off, he suggested in the interview). "I think he (Khan) has done a very bad job on terrorism", Trump told The Sun newspaper.
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Of Johnson, he said: "I have a lot of respect for Boris".
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"I do not think it's good for Europe and I don't think it's good for our country", Trump said. "It's called fake news".
"I said, 'I want to apologise because I said such good things about you, ' And she said, 'Don't worry, it's only the press, '" Trump said of their purported conversation. "When the president speaks about immigration, you will repeatedly hear him put it in the sense of a threat, a security threat specifically, and that's also how he framed it when he was talking about it in Europe". I haven't been there in a long time.
"They all showed up on the 9th hole, overlooking the ocean, and I said what's going on, and all they wanted to talk about was Brexit".
The president arrived in the United Kingdom on Thursday but is largely circumventing the capital and the massive protests against him. Look at what is going on in London.
London Mayor Sadiq Khan said the demonstrations are not anti-American but rather reflect opposition to "the politics of fear and despair". "Relationship is very important". The president also blamed immigration for the rise in violent crime in the city.
Recalling that visit during the press conference on Friday, he said there had been "an unbelievably large number of reporters there", adding: "I guess everybody was there because of Brexit". "I think you are losing your culture".