Asked if May should stay in power, Trump said "that's up to the people". He replied: "Yes. We will make everything possible - if the President wants to do something we will make it possible".
The New Zealand dollar rose against the British pound to the highest level in nearly two weeks after UK Foreign Secretary Boris Johnson became the latest minister to resign from Theresa May's Conservative government over her Brexit plans.
"I maybe will speak to him when I get over there", said Trump, who arrives in Britain on Thursday and is set to hold talks with May and meet with Queen Elizabeth II on Friday. "I've always liked him", Trump said as he departed from the White House.
Mr Trump told reporters: "He's been very nice to me".
US Ambassador to Britain Woody Johnson on Wednesday rowed back on President Donald Trump's comment that Britain was in "turmoil" because of Brexit-linked political upheaval.
Trump's week-long trip to Europe includes a meeting in Brussels with North Atlantic Treaty Organisation partners, who he has accused of not paying their way, and a summit with Russian President Vladimir Putin in the Finnish capital Helsinki. "If you actually look at the timeline between Eurodollar's slide and sterling's slide, the two are very much going hand-in-hand", said Alan Ruskin, global head of currency strategy at Deutsche Bank.
Recall that yesterday, June 9, the British foreign Secretary Boris Johnson, resigned.
Asked about the remarks, Mrs May's official spokesman said: "The Prime Minister is looking forward to showing the President the United Kingdom and is confident that he will leave with a very positive impression".
But he praised Mrs May as a "very tough negotiator" and described her as an "incredible woman" who is "doing a fantastic job".
'I like Boris Johnson. "So I think that symbolises how he considers the importance of her leadership in this country right now".
He went on to say Mr Johnson, who quit as foreign secretary over the Chequers' plan, was "a great representative for your country". "I think he's got what it takes".