The meeting took place in the wake of an explosive newspaper interview in which he said the Prime Minister's Brexit plans would kill off a trade deal with America and Boris Johnson would be a "great prime minister".
"I would say I would give our relationship in terms of grade the highest level of special", Mr Trump said.
Donald Trump's explosive interview with The Sun has been criticised by many United States news websites and newspapers. "She's a total professional because when I saw her this morning, I said: "I want to apologise, because I said such good things about you".
He also suggested Boris Johnson, who quit as foreign secretary this week in protest at May's Brexit proposal, would make a good prime minister.
Trump told the newspaper he felt unwelcome in London because of protests, including plans to fly a giant balloon depicting him as an angry baby.
Trump also blamed recent terrorist attacks there on Khan, who is a Muslim.
"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 a tremendous thing", he said.
Reporters are likely to question Mr. Trump about his commitment to North Atlantic Treaty Organisation, given his recent criticisms of the organization, and about his upcoming meeting with Putin.
Trump added that May's "soft" blueprint for the U.K.'s future dealings with the European Union would probably "kill" any future trade deals with the United States.
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Russian Federation has continually denied their alleged meddling before Trump's shocking win over Clinton. The White House said the release of the charges would not affect the summit.
For her part May, in a Facebook post published before Trump's arrival in the United Kingdom and his Sun interview, insisted that "we are having good discussions with countries we would aim to sign trade deals with, including the USA, as I will discuss with President Trump when he arrives in the United Kingdom on Thursday".
They reconvened for a lunch meeting on Friday, which was followed by a joint press conference.
The i reports that 100,000 people took to the streets of London to protest against the visit of Mr Trump.
"The spirit of friendship and cooperation between our countries, our leaders and our people, that most special of relationships, has a long and proud history", she said, adding that the United States was "not just the closest of allies but the dearest of friends".
"I'm right in the middle of it".
Khan said pro-Trump supporters would march on Saturday, although some were present on Friday, separated from the main demonstration by police.
In one of the milder reactions, Universities Minister Sam Gyimah tweeted: "Where are your manners, Mr. President?" "Very complicated negotiation, and not an easy negotiation, that's for sure", Trump added, in what appeared to be a further attempt to appease the British prime minister.
"I was very saddened to see he was leaving government and I hope he goes back in at some point".
Repeatedly speaking in support of the PM - he said he'd enjoyed spending so much time with her over the past two days.