"Interestingly, what the president also said at that press conference was 'don't walk away, '" May continued.
"I'm saying that now so that when I go into negotiations with you people, I'm going to try and top you, you're going to try and top us. I said well it's too early to say but right now I say we're competitors", he said.
Mr Trump used an interview ahead of his United Kingdom visit to renew his personal feud with the London Mayor, attacking him over the wave of terror atrocities and accusing him of doing "a bad job".
Some pro-Brexit Conservatives fear that a deal could emerge that leaves Britain tightly bound to European Union rules and represents a Brexit in name only. The U.K. portion of the trip was overshadowed by explosive and undiplomatic remarks he made about May's leadership, especially her handling of the Brexit negotiations.
She defended her blueprint for Brexit and urged her critics to back it.
"I would say I would give our relationship in terms of grade the highest level of special", Mr Trump said. I am just saying I think he would be a great prime minister. "There comes an inflection point, the Chequers deal was an inflection point, we will have to see what happens", Bannon said.
"The general direction of policy will leave us in at best a weak negotiating position, and possibly an inescapable one".
Mr Rees-Mogg said Mrs May had apparently abandoned her "red lines" that had won her the support of the party in March.
Farage, a member of European Parliament and former leader of the U.K. Independence Party, said Trump chose to "intervene" for two reasons: he believes in Brexit and he feels the USA has been let down. It means we have got benefits out of this deal.
"Or we could have said: 'OK let's look at moving forward, let's look at an alternative proposal, ' which we have put forward".
"We're back to what civil servants wanted a year ago, the advice they were giving then, of something like the EEA (European Economic Area) membership plus something like the customs union".
He also labeled the interview with The Sun as fake news and said it did not include the positive things he had said about the prime minister.