Answering a reporter's question over whether May would stay in power, Trump said as he set off on a trip to Europe, "That's up to the people. I get along with her very well, I have a very good relationship."
May is grappling with a political crisis in London after Brexit Secretary David Davis and her foreign minister, Boris Johnson, resigned over her proposals for a “business friendly” Brexit, or exit from the European Union.
Trump, who said he has not spoken with May since the resignations, described Johnson as a "friend of mine" and said he might speak with him during the trip.
"He's been very, very nice to me, very supportive. Maybe we'll speak to him when I get over there. I like Boris Johnson. I've always liked him," Trump said as he departed from the White House.
Johnson, the face of Brexit for many British voters, said in his resignation letter that May was proposing a "semi-Brexit." Contact with him by the U.S. president during his visit would be seen by many as an insult to May.
"Brexit should be about opportunity and hope," Johnson said in his letter to May on Monday. "That dream is dying, suffocated by needless self-doubt."
Trump's victory in the 2016 presidential election shocked British diplomats in Washington and relations between May and Trump have been strained at times. Anti-Trump protesters are expected to take to the streets of London during his visit to Britain.
The enduring image of May's visit to the White House in January 2017, when she became the first foreign leader to meet the president after he took office, was Trump taking May's hand to help her down the steps of the White House colonnade.
Trump's week-long trip to Europe includes a meeting in Brussels with NATO partners, who he has accused of not paying their way, and a summit with Russian President Vladimir Putin in the Finnish capital Helsinki.
In between, he will be in Britain, with a black tie dinner hosted by May on Thursday and a working visit with the prime minister on Friday.
"I have NATO, I have the UK, which is in somewhat turmoil, and I have Putin," Trump said of his trip. "Frankly, Putin may be the easiest of them all. Who would think?"
