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Fresh from sending NATO into crisis talks and ahead of a summit with Kremlin chief Vladimir Putin, Trump shocked Britain's political establishment when he criticised May's plans for ties with the European Union after Britain leaves in March.
In a newspaper interview published just hours before holding talks with May, Trump said her Brexit strategy would "kill" any chance of a trade deal with the US and said she had not listened to his advice on how to negotiate with the EU.
But, as the two leaders stood together for a press conference in the garden of May's grand 16th-century official residence Chequers, Trump said the British leader was doing a "fantastic job", added it was up to her how to conduct Brexit, and that a free trade deal was very much on the table.
Relations had never been more special, he said, and any criticism was "fake news".
"Once the Brexit process is concluded and perhaps the UK has left the EU, I don't know what they're going to do but whatever you do is OK with me, that's your decision," Trump said.
"Whatever you do is OK with us, just make sure we can trade together, that's all that matters. The United States looks forward to finalising a great bilateral trade agreement with the United Kingdom. This is an incredible opportunity for our two countries and we will seize it fully," he said.
At the same location a week ago, May finally won agreement for her Brexit plans from her cabinet after two years of internal wrangling, but within days, two senior ministers had quit, departures which Trump said earlier in the week had left Britain in "turmoil".
Some lawmakers in her deeply divided Conservative Party have cast May's "business-friendly" Brexit plan as a betrayal that would leave Britain too close to the EU and warned that she might face a leadership challenge.
May's formal proposals were published on Thursday, but hours later the Sun newspaper published an interview with Trump where he appeared to side with the prime minister's critics.
"If they do a deal like that, we would be dealing with the European Union instead of dealing with the UK, so it will probably kill the deal," he told the Sun. "I would have done it much differently. I actually told Theresa May how to do it, but she didn't listen to me."
Asked about that interview, Trump said he had not criticised May, lavishing praise on "a terrific woman", who was smart, tough and capable.
"This incredible woman right here is doing a fantastic job, a great job," he said. "She's a total professional because when I saw her this morning, I said: 'I want to apologise, because I said such good things about you'. She said: 'Don't worry, it's only the press'."
May, likewise, glossed over the comments in the Sun, saying her deal provided a platform for an ambitious free trade deal.
Trump's remarks to the Sun were the most biting any US president has ever made on visit to Britain. However, under the blue skies of the Chequers' garden, he said their relationship was "the highest level of special".
However, while Trump and May exchanged warm words, tens of thousands of protesters marched against the US president through central London, bringing much of the British capital to a standstill. It was one of the more than 100 demonstrations planned across the country during his four-day stay.
"The message we came here to give today is that Trump is not welcome in Britain," said shopkeeper Grish Gregoran, 58, who took the day off to attend. "We wanted to embarrass him and I think we have done that today.
Trump has also frequently angered British politicians and has been involved in social media spats with London's Muslim mayor Sadiq Khan who Trump said had "done a very bad job on terrorism".
Late last year, May herself criticised Trump for retweeting a message by a member of a British far-right group, and the speaker of parliament has said the president would not be welcome to address the chamber.
After leaving Chequers, Trump travelled to Windsor Castle to have tea with Queen Elizabeth. He was heralded by military bands on his arrival at the 92-year-old monarch's home where her grandson Prince Harry married US actress Meghan Markle in May.
He later flew to Scotland where he is staying at his Trump Turnberry golf course. The protests reached him there, when a paraglider bearing the logo of environmental campaign group Greenpeace swooped within some few hundred yards of the president as he stood outside the golf course's hotel, television pictures showed.
He will stay in Scotland until Sunday when he heads to Helsinki for talks with Russia's Putin. Trump said he would bring up the issue of nuclear disarmament with Putin.
However his trip to meet Putin is set to be overshadowed by news that a US federal grand jury has indicted 12 Russian military intelligence officers on charges of hacking the computer networks of 2016 Democratic presidential candidate Hillary Clinton and the Democratic Party.
"We have this stupidity going on, pure stupidity, but it makes it very hard to do something with Russia because, anything you do, it's like: 'Russia, oh he loves Russia'," Trump said at the press conference before news of the indictment.
"I love the United States but I love getting along with Russia and China and other countries."