In a press conference on Friday that revolved mostly around Trump's criticism of May, the American president claimed repeatedly that he was misquoted. Trump, whom Johnson has effusively complimented, told the Sun he'd make a good prime minister.
Without the backing of her own ranks and with a working majority of just 13, the prime minister will need to rely on opposition parties, Politico reported.
Speaking specifically about the future of trade between the two countries, following his comments to The Sun that the Brexit white paper could threaten a trade deal between the two nations, President Trump said he didn't mind what happened with Brexit as long as the USA got a good trade deal with the United Kingdom.
A weekly recap of the top political stories from The Globe, sent right to your email. "She wanted to go a different route", Trump said, adding that May "didn't listen".More news: Trumps get royal treatment at tea with Queen Elizabeth II
"I think she is a very tough negotiator, she is a very, very smart and determined person", the president commented, adding he would rather have May as his friend than his enemy.
The US president questioned her handling of Brexit in an interview with The Sun tabloid, published on Thursday.
Trump also claimed Khan - with whom he has clashed in the past - has "done a very bad job on terrorism".
Sources have revealed particularly nasty remarks Trump has reportedly made about May.
As Mr Trump and Ms May spoke, thousands of protesters marched through central London, one of more than 100 demonstrations against the President planned during his stay.
"I didn't criticise the prime minister".More news: Prince Louis, Prince William and Kate’s third child, is christened
Their joint press conference came just hours after Trump had rubbished May's Brexit plans and warned that it will "kill" chances of a trade deal between the U.S. and Britain.
"Whatever you do is OK with us, just make sure we can trade together".
"But personally, I don't think we should have been rolling out the red carpet for Donald Trump". "I was opening Turnberry the day before Brexit". Then he left to have tea with Queen Elizabeth II at Windsor Castle.
'I was very saddened to see he was leaving government and I hope he goes back in at some point. "Our countries are meant to have a special relationship, yet you publicly criticized the prime minister's policy and her personally for not listening to you this week".
During the press conference, Mr Trump - who regularly accuses the USA media of "fake news" over its coverage of him - also clashed with a reporter from the American NBC network, describing it as "possibly worse than CNN".
Mr Trump said he apologised to Mrs May over the Sun front page story, and she replied: "Don't worry it's only the press".More news: Thai soccer team and coach to be discharged from hospital next week