Trump on Tuesday also said Britain's former foreign secretary Boris Johnson, who resigned on Monday over May's softer line on Brexit, was "very supportive" and "a friend".
Trump made the remark as he set off on a trip to Europe which includes a visit to Britain where he will hold talks with May who is now wrestling with a political crisis after two top ministers quit over her plans for Brexit.
May appears to have seen off an immediate challenge to her leadership from malcontents within her Conservative Party but Trump's comments ahead of the trip - that Britain was "in somewhat turmoil" and that it was up to the people if she stayed in power - fanned the sense of political crisis.
"I like Boris Johnson".
Trump has long voiced his support for Brexit, saying it was part of a global uprising that ultimately thrust him to power, and he was at his Scottish golf resort the day after Britons voted to leave the European Union, saying the outcome was a "great thing".
I like Boris Johnson. The former foreign secretary quit on Monday in protest of the prime minister's approach to Brexit.
Mr Trump told reporters: "He's been very nice to me".
Diplomatic disconnect with North Korea spells trouble for Trump
Pompeo, who is now in Tokyo , is expected to meet with Japanese and South Korean counterparts to brief them on his visit. The lawmaker's comments come one-day after North Korea criticized the US for their push for denuclearization.
Hazard: Real Madrid reportedly readying 170m-euro offer
He never drops his standards, he's a team player with a winning mentality and he can play for any demanding club in the world. Chelsea have told potential suitors that they will not sell Eden Hazard for anything less than €200 million this summer.
Chelsea FC’s first signing under Maurizio Sarri revealed
Negotiations for the highly-rated manager's payoff have accelerated over the last 48 hours and are nearly completed. It is likely that Conte himself will now take a short break from football while considering his future.
A U.S. Dollar note is seen in this June 22, 2017 illustration photo.
Trump's victory in the 2016 presidential election shocked British diplomats in Washington and relations between May and Trump have been strained at times.
The president and Mrs Trump then headed to Scotland where he is expected to spend the weekend on a private visit to his golf resort at Turnberry in Ayrshire.
Speaking as he prepared to depart for a European trip in which he will meet the Prime Minister at the North Atlantic Treaty Organisation summit in Brussels before his first visit to the United Kingdom as U.S. president, Mr Trump insisted he got along with Mrs May "very well".
"She was the first foreign dignitary to visit the USA when he became president".
And Mr Trump suggested he may have an easier time talking to Russian president Vladimir Putin in Helsinki next week than with Mrs May during his visit to Britain beginning on Thursday.