However, the president also suggested that the dispute with Khan was personal and that the mayor had shown disrespect to him by allowing a 20-foot "Trump Baby" balloon - an orange likeness of Trump wearing a diaper - to fly over London protests during the president's visit.
They will hold talks at the Prime Minister's country residence of Chequers on Friday where Russia, Brexit and the Middle East will top the agenda.
Mr Trump cancelled a planned visit to open the newly-relocated embassy at the beginning of the year, saying it was a "bad deal" to move from Grosvenor Square in the prestigious Mayfair district of central London to what he described as an "off location" at Nine Elms, south of the Thames.
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.
The first of the London protests against Donald Trump's visit outside Winfield House in Regents Park - demonstrators planning to make as much noise as possible overnight to stop Trump getting a good night's sleep!
"I look at cities in Europe, and I can be specific if you'd like. I haven't been there in a long time", Trump said. "But when they make you feel unwelcome, why would I stay there?"
She had used the Blenheim black tie dinner with political and business leaders to press Mr Trump on the benefits of a free trade deal after Brexit.
"I think he's got what it takes, and I think he's got the right attitude to be a great prime minister".
Sarah Elliott, chairwoman of Republicans Overseas UK, told CNN she did not think Trump would be fazed by the stunt.
May's plan "will definitely affect trade with the United States, unfortunately in a negative way".
"I don't think that's the case, and I think that the mood last night at the Blenheim dinner was so fantastically positive it focussed a lot on trade".
He said it was different to when former USA president Barack Obama tried to help the Remain campaign during the 2016 European Union referendum campaign by saying the United Kingdom would be at the "back of the queue" for a trade deal with the U.S. if left the EU.
Soon after she published her controversial Brexit White Paper which has divided MPs within her own Conservative Party, May sought to win over the USA president after the Britain exits from the European Union in 2019.
Two senior cabinet ministers, including former foreign secretary Boris Johnson, resigned this week over the plan, saying it keeps the country too aligned to the European Union and does not respect the wishes of the people who voted to leave the EU in the 2016 referendum.
Trump has clashed in the past with May - even though she is a conservative who shares his view that defense spending should be raised - and with her predecessor, David Cameron, who challenged Trump's anti-Muslim campaign stance as "divisive, stupid and wrong". "With a lot of resignations", Trump told a news conference at the North Atlantic Treaty Organisation summit in Brussels.
But Mr Trump said the prime minister is a "very good person" denying claims he called her a bossy schoolteacher, or said she was boring.
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