Mr Trump has sparked a backlash from UK politicians after telling The Sun the PM's Brexit plan would "probably kill" a UK-US trade deal.
In an interview with the Sun published late Thursday, as he dined with May, Trump said her proposal to execute a so-called "soft Brexit", maintaining ties with the European Union, was wrong and would torpedo a USA trade deal.
Trump also said that Boris Johnson, who had resigned as foreign secretary on Monday in protest of May's recent announcement of a plan for Brexit, was "a very talented guy" who "would be a great prime minister". "I told her, 'I want to apologize, because I said such good things about you.' " Trump said May told him, "Don't worry, it's just the press".
Trump has always been a supporter of Brexit and has expressed enthusiasm for a wide-ranging trade deal with Britain after it leaves the European Union, something heralded by Brexit supporters as being one of the great benefits of exiting the bloc.
Activists inflate a giant balloon depicting US President Donald Trump as an orange baby in north London on July 10, 2018 ahead of a demonstration in London to coincide with the visit of the US president.
GMB/status/1017669404115587077?"Of course we stand shoulder to shoulder in adversity, and it was really comforting when Americans sent messages of support when we had terrorist attack past year", Khan said, "but when we think you're wrong we should say you're wrong - that's what a special relationship is all about". "I think he is a great representative for your country", Trump told the newspaper.
Hurricane Chris could impact southeastern Newfoundland Thursday
Tropical Storm Chris is shown off the eastern coast of North and SC , U.S., in this satellite image July 9, 2018 at 16:12 UTC. Over the next 48 hours there is only a 10 per cent chance of formation, according to the NHC.
"I would say I would give our relationship in terms of grade the highest level of special", Trump said.
Queen Elizabeth later welcomed the president and First Lady Melania Trump Friday for a formal tea at Windsor Castle.
Standing next to May during a joint news conference at the British Prime Minister's official country house, Chequers, Trump announced he had at least started to apologize earlier in the morning.
Asked if the row jeopardises that bond, he said: "It takes two to tango, and I'm not tweeting President Trump or saying beastly things about him". I am assuming that his mum told him that when you go to someone's house you do not insult the host.
During the press conference, May also thanked Trump for his support over Russia which Britain has blamed for a nerve agent attack on a former Russian spy in southwest England in March. So I think allowing millions and millions of people to come into Europe is very, very sad. I haven't been there in a long time.
Trump expressed his admiration for Johnson in an interview with The Sun, published just hours before a scheduled meeting with Mrs May at her Chequers residence.
He also refused to take a question from CNN, saying: "CNN is fake news, I don't take questions from fake news".