President Trump and British Prime Minister Theresa May talked up the relationship between their two countries Thursday, amid reports that the ties between the two leaders have become strained in recent months.

The two leaders spoke at the World Economic Forum in Davos, Switzerland, where they downplayed rumors that their relationship had become frosty amid a number of high-profile controversies. Trump said he wanted to correct a “false rumor” that they were not getting along.

“[May] and myself have had a really great relationship, although some people don't necessarily believe that. But I can tell you it's true,” Trump told reporters. “I have a tremendous respect for the prime minister and the job she's doing. And I think the feeling is mutual from the standpoint of liking each other a lot.”

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“We are very much joined at the hip when it comes to the military. We have the same ideas, the same ideals,” he said before turning to speak to May directly. “There's nothing that would happen to you that we won't be there to fight for you.”

May was similarly glowing in her praise of what she called a “really special relationship between the U.K. and the United States.”

“In fact... stronger because we both face the same challenges across the world, and as you say, we're working together to meet those challenges,” she said.

10 Downing Street later confirmed to Fox News that officials are working together on finalizing the details for a visit by Trump to the U.K. this year.

May was the first foreign leader to visit the Trump White House after Trump was inaugurated. Through the 2016 campaign, Trump had expressed continued support for a U.S.-U.K. trade agreement in the wake of Britain’s decision to leave the European Union.

But ties between the two countries became strained in the wake of Trump’s travel ban, which May criticized and which led British left-wing politicians such as Labour Party leader Jeremy Corbyn and London Mayor Sadiq Khan to call for May to yank the offer of a Trump state visit to Britain made during her visit to Washington.

While May has rebuffed those calls, she has continued to express disagreement with a number of decisions by the Trump administration, particularly on the Iran nuclear deal and the decision to move the U.S. embassy in Israel to Jerusalem -- which her office described as "unhelpful."

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Tensions bubbled over in November when Trump retweeted anti-Muslim videos from a U.K. far-right group. This month Trump canceled a visit to London to open a new embassy, claiming it was because it was a bad deal, although there has been speculation that it was due to heightened opposition in the U.K. to his visit.

The public display of close ties came on the heels of an article in Bloomberg News describing a “dysfunctional” relationship in which Trump dominates conversations and has complained to May about his coverage in the British press.

Additionally, the article reports that May’s team now regrets their “nightmare” decision to extend to Trump the offer of a state visit.