Story highlights "The Prime Minister and myself have had a really great relationship," Trump said

Trump and May held a bilateral meeting in Davos, Switzerland

Davos, Switzerland (CNN) President Donald Trump on Thursday began his formal meetings at an economic summit here by hailing his relationship with British Prime Minister Theresa May, a friendship that has seen highs and lows over the first year of Trump's presidency.

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.

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