The comments come ahead of his controversial four-day visit to Britain.
Trump also expressed disappointment with May's handling of Britain's withdrawal from the EU. A lot of people like me there.
Mr Trump patted Mrs May's hands as they began to take their first steps up the stair case. "But maybe they're taking a little bit of a different route, so I don't know if that's what they voted for".
After months of controversy surrounding his visit to the UK, Donald Trump will finally meet with Queen Elizabeth at the end of this week.
At a welcoming garden party, the Beatles track "We can work it out" played in the background.
The American president reveals in an interview with The Sun newspaper that he has been told about a 20-foot "Trump baby" balloon that will be flown above Parliament Square on Friday as protesters march.
But some 77 per cent of Britons have an unfavourable view of Trump, according to a poll by YouGov with 1,648 respondents. He has done a bad job. Picture: GettyAmnesty International unveil a banner on the Vauxhall Bridge.
Trump went after London Mayor Sadiq Khan, claiming he "has done a bad job on terror".
Trump then travelled by helicopter to the USA ambassador's residence in London.
"Our trade and investment relationship is unrivalled - we are the largest investors in each other's economies and every day a million British people go to work for U.S. companies in the United Kingdom and a million Americans go to work for United Kingdom companies in the U.S.", May said.
She added it was "also an opportunity to tear down the bureaucratic barriers that frustrate business leaders on both sides of the Atlantic".
May weathered the resignations of her Brexit and foreign ministers earlier this week over the proposals.
Speaking at an impromptu press conference after a North Atlantic Treaty Organisation summit in Brussels Trump said the British people shared his concerns on immigration, claiming "that's why Brexit happened".
On Saturday he will fly up to Scotland to play golf at one of his resorts and his son Eric landed in the family's "Trump Force One" private jet at Aberdeen this morning, before flying to Helsinki to meet Vladimir Putin on Monday.
Russian Federation has strongly denied the charge.
The pair will then travel to Chequers - the PM's country residence in Buckinghamshire - for talks with the foreign secretary.