Sitting alongside his host at the start of talks at May's country retreat of Chequers, Trump told reporters: "The relationship is very, very strong. He's been saying very good things about me as president". "But Boris Johnson, I think would be a great Prime Minister".
Trump's comments saw the value of the pound plunge on currency markets.
On Friday, Trump said that at a gala dinner at Blenheim Palace the night before he and May spoke for nearly 90 minutes and had "probably never developed a better relationship".
The Independent also takes up the president's attempt to go back on what he apparently told the Sun, with a somewhat tongue-in-cheek effort: "Trump's backtrack - the "highest level of special".
Another wrote: "I think I can hear Dusty singing "The Look of Love".
But then Trump made the ridiculous claim himself, again. It's an accurate representation of his politics which are so immature.
He said Mr Trump's remarks on trade were a "perfectly reasonable thing for an American president to say".
"She wanted to go a different route. And that is fine", he said.
Trump said the interview published by the Sun omitted his praise of May, and that his staff had taped the interview: "It's called fake news and we solve a lot of problems with the good old recording instrument". May of going soft on Brexit and argued that her strategy would keep the country too aligned with the EU.
Surprise! Kate Middleton makes appearance with royal family at RAF celebration
She attended her brother-in-law's wedding in May, Trooping the Colour in June, and now the RAF centenary commemorations. Come Saturday, all eyes will be on her sister, Kate, who will join Meghan in cheering on Serena Williams .
The government published its blueprint on Thursday calling for closer trade ties with the European Union after it leaves the bloc next March.
Trump also issued a warning to the European Union, telling it to "be very careful" of increasing immigration into the region, as he described a global backlash to migration. It was during that trip to Washington that she invited him to the UK.
Donald Trump and his granddaughter Kai visit Trump International Golf Links in Aberdeen, Scotland, on June 25, 2016.
He repeated the falsehood during a press conference with UK Prime Minister Theresa May.
"The president likes and respects Prime Minister May very much".
By Friday afternoon, Mr. Trump appeared to backtrack, saying he'd had an opportunity to learn more about Ms.
Putin's government is accused by May's of unleashing a deadly nerve agent in the English city of Salisbury.
After almost 18 months in office, Trump finally visited the United Kingdom this week, allowing protesters who've been preparing more than a year for this to unleash their fury.
From 11am, tens of thousands of demonstrators began to gather in central London to protest against the presidential couple's "working visit".
Melania Trump visited veterans on Friday at London's Royal Hospital Chelsea where she also met local school children, accompanied by May's husband Philip.