"The idea that we would park our rights and privileges and freedoms because it may cause offence to a USA president, I think people in London and the United Kingdom would find objectionable as indeed would Americans", the mayor said.
The two leaders spoke after meeting at Chequers, the prime minister's country estate. Why the drastic step?
"I said very good things about her" in the interview, Trump said.
GMB/status/1017669404115587077?"Of course we stand shoulder to shoulder in adversity, and it was really comforting when Americans sent messages of support when we had terrorist attack previous year", Khan said, "but when we think you're wrong we should say you're wrong - that's what a special relationship is all about".
He said the way she is proposing to break from the European Union might hurt the USA -U.K. trade relationship.
The interview also touched on London Mayor Sadiq Khan, who Trump has criticized, including in the wake of apparent terrorist attacks on the UK's capital city.
The press conference comes after Trump's interview with The Sun, in which Trump doubled down on criticism of May's approach to handling Britain's departure from the European Union.
However, he later said Ms May was doing a "fantastic job".
"I would say she actually went the opposite way".More news: Meghan accused of breaking royal protocol
In response to a question about future trade after Brexit, Trump said: "I don't know what Britain is going to do but whatever you do is OK by me".
"I think he has done a bad job on crime, if you look, all of the disgusting things going on there, with all of the crime that is being brought in".
"I guess when they put out blimps to make me feel unwelcome, no reason for me to go to London", the president said.
If Trump said it, it's not clear when or where.
'She held his hand as she went up the steps at Blenheim Palace with him after she had heard all those things he was saying about her. They weren't in the headline of the story, he said, so he didn't see them.
On Boris Johnson, the former Foreign Secretary who has been such a thorn in Mrs May's side, he said he was a "a very talented guy", adding: "I like him a lot".
"If you reported them that's good", Mr Trump told the political correspondent.
Trump is due to meet Putin, who has rejected the nerve agent claims, at a summit when he finishes his four-day visit to Britain, and said he would raise the issue of reducing nuclear weapons. "I would describe it as a love fest between the President of the United States and the British Prime Minister, in terms of their two countries", Ruddy said in an interview with CNN's Chris Cuomo on "Cuomo Prime Time". That's a value judgment people can make for themselves.