Donald Trump will visit the United Kingdom “later this year”, Downing Street has announced.
The US President and prime minister held talks at the World Economic Forum in Davos on Thursday afternoon.
Speaking to reporters, Trump attacked what he called the “false rumour” that he did not like May and said the pair were “on the same wavelength in every respect”.
May added that she and Trump had a “great discussion” in their meeting and praised the “really special relationship” between the US and UK.
No.10 said British and American officials were now “finalising the details” of a visit by Trump to the UK by the end of 2018.
May’s decision to offer Trump a formal state visit shortly after his election triggered a significant backlash in the UK - with MPs demanding it be cancelled.
Trump told reporters that the US and UK had “the same ideas” and “the same ideals”.
Sitting alongside May following a private meeting, Trump said he had “tremendous respect” for the prime minister and that the “feeling is mutual”.
He added there would be a “tremendous increase in trade between our countries”.
May and Trump’s relationship appeared to sour after Trump retweeted the far-right Britain First and then admonished the prime minister for not focusing on “terrorism”.
Speaking in Davos, Trump said: “The prime minister and myself have had a really great relationship, although some people don’t necessarily believe that.
“But I can tell you I have a tremendous respect for the prime minister and the job she is doing and I think the feeling is mutual from the standing point of liking each other a lot. We are on the same wavelength in every respect.”
The President added: “There was a little bit a of a false rumour out there I just wanted to correct it.”
Trump said on foreign affairs, he and May had “the same ideas, the same ideals.
“There is nothing that would happen to you that we won’t be there to fight for you, you know that.”
May said: “We continue to have that really special relationship between the UK and the US, standing shoulder to shoulder because we’re facing the same the same challenges across the world and as you say, we’re working together to defeat those challenges and to meet them,” she said.
“And alongside that working for a good trade relationship in the future which will be to both our benefits so the US and the UK both do well out of this and it’s been great to see you today.”
Downing Street said Trump and May discussed a range of issues in their meeting, including Iran and Syria.
A No.10 spokesman said: “The Prime Minister updated the President on the good progress which had been made in the Brexit negotiations so far. The two leaders reiterated their desire for a strong trading relationship post-Brexit, which would be in the interests of both countries.
“The PM and President concluded by asking officials to work together on finalising the details of a visit by the President to the UK later this year.”