"You seem rather to have changed your tune from what you said earlier this week, when you said that on the current Brexit plan, that would probably kill the possibility of a trade deal with the UK", BBC political editor Laura Kuenssberg remarked.
Mr Trump told reporters: "He's been very nice to me".
Trump praised May's rival, Boris Johnson, and said the conservative, who is similarly blunt-spoken like Trump, would make a great prime minister.
London Mayor Sadiq Khan, who was criticised by Trump in the Sun interview for failing to control crime and prevent militant attacks, gave his blessing for the blimp to be flown and rejected suggestions this showed a lack of respect to the us president.
Protesters took the streets in London to demonstrate against the president's visit - and in Parliament Square, a Trump baby blimp was raised up in the air.
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Trump also said that he "would have done it much differently" in reference to the Brexit plan. "I actually told Theresa May how to do it but she didn't agree, she didn't listen to me", Trump said of Brexit. "I don't take questions from CNN".
A spokeswoman for the Institute of Directors said: "The prospect of a trade deal with the USA is attractive to business, so the President's more optimistic comments are welcome. I never said anything bad about her", Trump said.
The US president apologised to Mrs May on Friday over an incendiary interview criticising her premiership, and hailed UK-US relations as the "highest level of special". I get along with her very nicely.
At a press conference later in the grounds of the PM's country residence, Mr Trump insisted he "didn't criticise" the Prime Minister and hit out at "fake news".
"I think it's fair to say that the white paper is an evolution of the United Kingdom's position and evolved some of the red lines they had until now", he said. And yes, the balloon was even approved by the City of London. I didn't think they put it in, but that's all right.
The Queen politely gave a beaming smile to her guests - despite thousands sharing their distain at his visit in a London protest - yet the couple snubbed the usual curtsy and bow which, although not protocol, is considered good manners.
"I think they like me a lot in the UK", Mr Trump had said in Brussels.