As he began a four-day visit to Britain on Thursday, Trump, a major supporter of Brexit, told The Sun that he had advised May to go about leaving the European Union in a different way but was ignored.
Trump also heaped praise on Boris Johnson, who resigned as foreign secretary this week along with Brexit Secretary David Davis in protest at May's strategy. I know they have had a lot of resignations. "I'm very strong on immigration". The White House press secretary, Sarah Sanders, insisted the president "likes and respects Prime Minister May very much". "As he said in his interview with The Sun, she is a very good person and he never said anything bad about her", Sanders said. Its key provision is a "customs arrangement" with the EU that would see the United Kingdom remain largely within the bloc's customs union.
At Thursday's press conference, he repeated an incorrect claim that the United States "pays for 70 to 90% of NATO".
Though Trump has not so far given specific details about what nuclear arms control treaties they would like to talk about, he and Putin are likely to discuss the possibility of extending the "New Start" treaty - a pillar of arms control. "She probably thought it was too brutal".
Trump's interview with The Sun was full of provocative statements.
But he also said "this incredible woman right here is doing a fantastic job, a great job and I mean that".
He said he successfully pushed for North Atlantic Treaty Organisation members to spend more of their budgets on defence and at a faster pace than expected.
"Whatever you do is OK with us, just make sure we can trade together, that's all that matters".
"The deal she is striking is a much different deal than the one the people voted on".
The last, brief meeting between Putin and Trump took place in November 2017 in Vietnam during an APEC summit.
"I'll absolutely bring that up, but it won't be a Perry Mason moment".
NATO, a pillar of the global order, emerged from a two-day confrontation with President Donald Trump on Thursday intact but distracted and shaken, a further challenge to the alliance as it faces an expansionist Russian Federation and growing authoritarianism among some of its own members.
Trump first met May Thursday night and the pair spoke for about 90 minutes and attended a state dinner.
Mr Khan said however he planned on being the "bigger man" over the feud and not rise to taunts by Trump.
Younger voters - 18-34-year-olds - backed Mr Trump publicising his views on Brexit by 54% to 40%, compared with opposition by 51% to 46% among those aged 55 and older.
Trump said Khan had done "a awful job" on terrorism and crime in the capital. The president suggested not all of his comments about May were printed by The Sun, and that the newspaper had omitted the positive things he said about the prime minister.
Trump has always been a Brexit supporter and has expressed enthusiasm for a wide-ranging trade deal with Britain after Brexit, something heralded by eurosceptics as being one of the great benefits of exiting the bloc.
THE FACTS: Trump has said this before; it's not true.
"He's really quite stung by the criticism he's been getting", Dunn said.
"When you look at what we have done in terms of Russian Federation, I guarantee that whoever it is in Russian Federation, they are saying: 'Oh, God, do we wish that Trump was not the victor".