He added that there was "a tremendous opportunity to double, triple, quadruple" trade between the United States and the UK.
But Anthony Gardner, who was former president Barack Obama's ambassador to the European Union, held nothing back in attacking Trump's attack on May as "totally unacceptable" and "unprecedented" in the middle of a high-profile visit.
Trump is making his first trip to Britain as president after a tense summit with North Atlantic Treaty Organisation leaders in Brussels and on the heels of ruptures in British Prime Minister Theresa May's government because of the crisis over Britain's exit from the European Union.
Trump also said the deal that May's government has proposed would "probably kill" any trade agreement with the US because Washington "would be dealing with the European Union" instead of with the United Kingdom.
"Whatever you do is OK with us, just make sure we can trade together, that's all that matters".
But he said May and her representatives have since reassured him that will still be possible.
"I think he has done a bad job on crime, if you look, all of the awful things going on there, with all of the crime that is being brought in", Trump said of Khan. I think they agree with me on immigration. The Prime Minister will host a dinner at Winston Churchill's birthplace Blenheim Palace, with some of businesses biggest names - thought to include Sir Jim Ratcliffe, founder of Ineos, Larry Fink, head of BlackRock, and Alex Gorsky, chief executive of Johnson & Johnson.
But in a rambling 50-minute press conference in which he claimed several new outlets including the Sun were "fake news", Mr Trump's comments took a less helpful turn when he confirmed he had offered the Prime Minister an unspecified "suggestion" on Brexit.
Sadiq Khan has said he will not rise to Donald Trump's "beastly" comments, as he urged Theresa May to stand up to the US President. He also criticised the scale of immigration into Europe, and said he was saddened by protests in London, adding that they made him feel unwelcome. "She should negotiate the best way she knows how, but it's too bad what's going on".
Mr. Trump's intervention was "very important, because if you can't do a trade deal with your closest ally, then who can you do a trade deal with?" said Jacob Rees-Mogg, a Tory MP who has been among the sharpest critics of Ms.
Ms. May also tried to right the ship, pointing out repeatedly that Mr. Trump now agreed with her that a trade deal with the USA will be possible under her strategy.
Referring to planned protests in the city on Friday, which will see a blimp flown of the president portrayed as a baby in a nappy, Mr Trump added: "I think [the mayor] has not been hospitable to a government that is very important".
"I think he thinks I'm doing a great job. Look around. You go through certain areas that didn't exist ten or 15 years ago".
However, Trump ruled out May pursuing "no deal" - a move favoured by hard Brexiteers - saying there was no way the Prime Minister could walk away from the Brussels talks without an agreement.
During opening remarks ahead of the joint news conference with May, Trump said he is "OK with" however the British decide to carry out Brexit, despite trashing May's "soft Brexit" blueprint in The Sun. By the time he'd left on Friday, Mr. Trump had changed course and praised Ms.
The Tory MP said the European Union's "arrogant" behaviour in Brexit negotiations would trigger a higher Leave vote if Britons were forced into a second referendum.