"She wanted to go a different route", Trump said, adding that May "didn't listen".
"They voted for us to take back control of our money, our law and our borders", she said.
"I saw that the president was nodding furiously last night as she was speaking last night and I'm sure there will be a very positive discussion between them today", he said.
"And unfortunately there was a story that was done, which was generally fine, but it didn't put in what I said about the prime minister, and I said tremendous things".
Trump also all but endorsed May's chief political rival within her own party, the recently resigned British Foreign Secretary Boris Johnson, calling him "a very talented guy", lamenting his resignation from May's Cabinet and saying he believes Johnson "would be a great prime minister" - though he insisted he was "not pitting one against the other".
Anthony Gardner, who was ambassador to the European Union to former president Barack Obama, said Trump's attack was "totally unacceptable" and "unprecedented" in the middle of a high-profile visit.
USA president Donald Trump then dealt a blow, saying May's plans would end any hopes of a trade deal with the US.
But over on social media, it's also triggered a new meme, which involves a certain current British prime minister - who has been pictured looking positively smitten with her new guest.
According to Politico, the key question is whether May's Tory opponents will try to keep pressure on May or whether they have the numbers and the intention to damage her government in an effort to get the Brexit they feel voters expect.
However, while Trump and May exchanged warm words, tens of thousands of protesters marched against the U.S. president through central London, bringing much of the British capital to a standstill. That is fake news.
Meanwhile, a poll by SkyData revealed 51% of people thought Trump was right to make his views of Brexit public.
After leaving Chequers, Trump was scheduled to have tea later with Queen Elizabeth at Windsor Castle, where her grandson Prince Harry married United States actress Meghan Markle in May before flying to one of his golf courses in Scotland. I would actually say that she probably went the opposite way.
We look at some of Trump's most outrageous claims. May to correct him by saying flatly: "We will be leaving the European Union and we are leaving on the 29th of March, 2019".
In London, demonstrators began gathering for a mass protest against Trump, beginning with the flying of a huge balloon of the president depicted as a crying baby outside the Houses of Parliament.