Seeking to rebut claims of a rift, Trump insisted that he and May are "of the same wavelength, I think, in every respect."
"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's doing and I think the feeling is mutual," Trump said.
It was the first of several meetings Trump will take in Davos, the mountainside village that is hosting the annual World Economic Forum this week.
Trump arrived earlier in the day after an overnight flight from Washington and a scenic helicopter journey over the Alps from Zurich.
He told reporters as he strode into the Congress Center in the central village that he expected a warm welcome from the globalist crowd gathered here.
Asked if he would be received well, Trump gestured to a large crowd gathered to watch him enter.
"I already am," he said.
Trump's presence at Davos has been met with a mixture of befuddlement and anxiety. His populist ideals aren't a natural match for the collection of chief executives, celebrities and heads-of-state who make the yearly trek to the snowy summit.
But even if Trump's brash, uncensored manner causes heartburn here, the massive tax cuts he signed at the end of last year have been welcomed among the collection of businessmen and financial CEOs.
May, who addressed the forum earlier in the day, had lobbied for a meeting with Trump after their relationship deteriorated over a series of sticking points, including Trump's retweeting anti-Muslim videos produced by a British nationalist group.
Trump has also delayed a state visit to London after May extended the invitation a year ago. He's likely to be met with large protests in the British capital if and when he does travel there.
Asked about the state visit, both May and Trump affirmed on Thursday the parameters of the trip were still under discussion.
Trump denied any fissures in his relationship with May during remarks at the conclusion of their meeting on Thursday.
"That was a little bit of a false rumor out there, I just wanted to correct it," he said. "We have great respect for everything you're doing, and we love your country."