US President Donald Trump insisted he did not criticise Theresa May in the interview that dominated the build-up to the two leaders’ press conference.
Mr Trump has sparked a backlash from UK politicians after telling The Sun the PM’s Brexit plan would “probably kill” a UK-US trade deal.
He also said Boris Johnson would make a “great prime minister”.
But after talks with Mrs May he claimed “tremendous things” he said about her had been left out of the Sun story.
He said the paper’s story was “generally fine”, but “it didn’t put in what I said about the prime minister, and I said tremendous things”.
“Fortunately, we tend to record stories now so we have it for your enjoyment if you’d like it,” he said.
“We record when we deal with reporters, it’s called fake news and we solve a lot of problems with the good old recording instrument.”
The Sun’s write-up of its interview, which was recorded, quoted him describing her as a “nice person” and that they get along “very nicely”.
Later in the press conference at the prime minister’s country residence, Chequers, Mr Trump verbally sparred with the Sun reporter who had interviewed him, Tom Newton Dunn.
Mr Newton Dunn told the president that his positive remarks about Mrs May had been included in the story.
“If you reported them that’s good,” Mr Trump told the political correspondent.
“Thank you very much for saying that.”
He added: “I didn’t think they put it in, but that’s all right.
“They didn’t put it in the headline, I wish they put that in the headline, that’s one of those things.”
On Mrs May’s reaction, he added: “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’.
“She said: ‘Don’t worry it’s only the press.’ I thought that was very professional.”
A spokesman for the Sun declined to comment on Mr Trump’s remarks about the paper’s story.