POTUS told her not to enter into negotiations with the European Union; instead, she should sue the bloc as part of her Brexit strategy.
Trump, who began a four-day visit to the United Kingdom on Thursday, will conclude the private leg of his tour in Scotland today to head to Finland for talks with Russian President Vladimir Putin in Helsinki tomorrow.
A bemused May turned him down.
Britain's Prime Minister Theresa May appears on the BBC's Andrew Marr Show in London, Britain July 15, 2018.
On Friday, in a joint press conference with the prime minister, he rowed back, saying a trade deal was "absolutely" possible and that it could be "great". Now, you add that into all the other things I've done, um, President Putin has to respect what we've done. "Sue the EU. Not go into negotiations - sue them".
It wasn't exactly clear what Trump meant, but the revelation capped a series of explosive and undiplomatic remarks Trump made this week about May's leadership - especially her handling of the Brexit negotiations - as he made his first official visit to Britain.
"He told me I should sue the European Union - sue the European Union - not go into negotiations, sue them".
Baker, who was a junior minister under Davis, claimed the Brexit Department was little more than a "Potemkin structure to [distract from] what the Cabinet Office Europe unit was doing for the Prime Minister".
Both leaders tried to brush aside Trump's incendiary language at a news conference Friday, insisting they were determined to pursue a post-Brexit pact.
Asked to rate US-UK relations, Mr Trump called them the "highest level of special".
Earlier, activists floated a six-metre-high blimp outside parliament depicting the USA president as an orange, snarling nappy-wearing baby.
"Everyone thought it was going to be 'Oh it's simple, we join or don't join, or let's see what happens'".
"When I say lovely, inside and out", Trump said.
In addition to criticizing May's handling of Brexit negotiations, Trump has gone after many of his European NATO allies for relying on the USA for trade and defence spending, and called the EU a trade "foe" in an interview with CBS on Saturday.
He played a few rounds of golf at his Turnberry golf course on the Ayrshire coast, where he arrived on Saturday after tea with Queen Elizabeth II at Windsor Castle.
And he's angry the PM went over his head with the Brexit white paper. That has infuriated fervent Brexit supporters, who see it as a bad deal. Along with Mr Johnson, the man who had been leading the Brexit negotiations, David Davis, also quit in protest. We now face continued harmonisation with the bloc's rules on goods.
He described her as a "Remainer who has remained a Remainer".
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