"We're on the same wavelength in, I think, every respect," Trump said on Thursday during their meeting in Davos, Switzerland, on the sidelines of the annual World Economic Forum.
"The prime minister and myself have had a really great relationship," he added. "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."
Post-Brexit trade relations between the two countries were high on the agenda. "One thing that will be taking place over a number of years will be trade. Trade is going to increase many times,” Trump said.
May replied that the "really special relationship" between the UK and US continued and they stood "shoulder to shoulder because we are facing the same challenges across the world."
Trump has not yet visited Britain since taking office a year ago over fears of mass protests, and has been involved in rows with the government over issues including trade and his re-tweeting of an anti-Muslim video posted by a British far-right group.
May offered Trump a state visit to Britain one year ago, when she became the first foreign leader to visit the White House after his inauguration.
Earlier this month, Trump cancelled a visit to the UK, criticizing the cost and location of the US embassy in London.
But British Foreign Secretary Boris Johnson suggested the decision to cancel the trip was prompted by the strong public and political opposition to Trump in Britain, warning that critics "seem determined to put this crucial relationship at risk."
Johnson also criticized London Mayor Sadiq Khan and the opposition Labour Party leader Jeremy Corbyn for opposing a presidential visit.
Earlier this month, Corbyn rejected the so-called “special relationship” between the US and the UK, saying that Washington is not the most important ally of London.
The Special Relationship is an unofficial term for the political, diplomatic, economic, military and cultural relations between the United States and the United Kingdom. It was first used in a 1946 speech by former UK prime minister Winston Churchill.