Mr Trump revealed at a press conference on Friday he had privately suggested Mrs May should activate a "brutal" option to come out with the best deal - which today Theresa May revealed to be a suggestion to "sue" the EU.
Speaking on the BBC's Andrew Marr show, Mrs May said the US President also advised her not to walk away from negotiations.
In an interview the Sun newspaper, published just hours before the two leaders held talks, Mr. Trump chided the "very unfortunate" results of the Prime Minister's proposals for Brexit and her negotiating tactics as Britain prepares to leaves the European Union in March next year.
Meanwhile Steve Bannon, a former adviser to President Donald Trump, says now is the time for former Foreign Secretary and leading Brexiter Boris Johnson to challenge May for her job. "Don't walk away from those negotiations because then you'll be stuck. If we don't, we risk ending up with no Brexit at all", she said.
Towering over the queen, Mr Trump and the monarch shared a few interactions as they reviewed troops at the royal castle in Windsor.
Man Utd striker Marcus Rashford issues positive England injury update
Or maybe that came when the English endured their shortest World Cup campaign two years earlier whey they were only in contention for eight days.
Seeking to strike a balance between those who want a smooth Brexit and those who fear staying too close to the EU's orbit, May sought the approval of senior ministers for her plans on July 6.
"Everyone thought it was going to be "Oh it's simple, we join or don't join, or let's see what happens", he said. "She wanted to go a different route", he said. At Sandhurst, Britain's elite academy where military officers undergo training, Trump watched a display, travelling later in the now customary helicopter to Chequers, the prime minister's country retreat in Buckinghamshire where he and May held talks. "As he said in his interview with The Sun she "is a very good person" and he 'never said anything bad about her, '" the White House responded.
"I said very good things about her" in the interview, Trump said.
"Or we could have said: 'OK let's look at moving forward, let's look at an alternative proposal, ' which we have put forward".
It is unclear how such a lawsuit would work for Britain, a member of the European Union, but Trump has often threatened lawsuits in dealmaking.
The Prime Minister acknowledged that there were strong feelings regarding the terms of Britain's withdrawal from the EU.