Trump's interview attracted sharp criticism from British MPs, many of whom described it as an insult to the British prime minister and the UK.
But the comments drew outrage from some British lawmakers and will make for an awkward atmosphere with May when the pair meet at her country retreat of Chequers for a working lunch, followed by a press conference.
Trump called the Sun story "generally fine" but said that some of his remarks were left out.
In a statement, a spokesperson for the Sun said the president had "essentially retracted" his claim that their interview was fake news.
They also undermine the prime minister as she faces speculation of a leadership challenge from eurosceptics in her Conservative party following the resignations of Johnson and Brexit secretary David Davis.
Humorous protests take flight in London during Trumps four day tour of the UK.
Trump's comments to The Sun were all the more surprising since he tried several times earlier on Thursday not to barge into the Brexit debate. That is fake news.
He insisted: "I said I thought it was going to happen and it did happen".
In response, Khan said it was "interesting" that Trump was "not criticising the mayors of other cities" which had also experienced terror attacks.
"The sense of betrayal in this country will be huge, and I very much hope that she's out of office before too long", Farage said.
But even before he arrived, the president criticized May's Brexit plan, said the country was in "somewhat turmoil" and that meeting with Russian President Vladimir Putin next week - the British premier's geopolitical enemy - would be easier than meeting with her.
However, Trump later said May was doing a "fantastic job".
"It's changing the culture; I think it's a very negative thing for Europe", he said, noting that it was not politically correct to say so, "but I'll say it and I'll say it loud". "She might well do what I suggested that she might want to do but it is not an easy thing".
Speaking specifically about the future of trade between the two countries, following his comments to The Sun that the Brexit white paper could threaten a trade deal between the two nations, President Trump said he didn't mind what happened with Brexit as long as the USA got a good trade deal with the United Kingdom.
The Prime Minister prefers a tightly-controlled approach to press conferences, delivering carefully-scripted lines to drive home her core message.
"The deal she is striking is a much different deal than the one the people voted on", Trump said in the interview, and added that he had told May to toughen up.
Excerpts from Trump's bombshell interview were published Thursday just as the president was scheduled to dine with May at the palace.
"It's also an opportunity to tear down the bureaucratic barriers that frustrate business leaders on both sides of the Atlantic", she said.
In the interview, Trump also renewed his criticism of London Mayor Sadiq Khan over last year's terror attacks in the capital, saying he had done "a bad job".
F1 sees distinguished manufacturers make a welcome return
It would also be nice to see a more competitive side to the sport, which usually sees one side dominate the entire season. The team is looking at Charles Leclerc from Ferrari, Marcus Ericsson or Antonio Giovinazzi who is a reserve for Ferrari.
Total integration of fitness apps may be the next step.
An example of a simple, natural replacement item in this instance is the Under Armour Gemini 3 RE smart shoes. Not their departure, by any means, but the total integration of their smart features into our everyday items.