After being prompted by a surprised Marr, May repeated: "Sue the European Union, not go into negotiations with them, sue them".
Trump said in an interview published on Friday that May had not followed his advice on Brexit - one of a number of comments that were seen as a damning critique of her exit plans and added fuel to the raging debate over May's plans to leave the EU.
"No, no - we're going into negotiations with them", May said she told the USA president.
Meanwhile, May went on to defend her controversial new White Paper for Brexit, which has shaken up her government with high-profile Cabinet resignations, and urged critics, both in and out of her own Conservative party, to back it.
He added that it was "too bad what is going on", and that her ultra-soft Brexit plans would "probably kill" a British-American trade agreement by leaving the European Union with too much control over Britain's economy for a deal to be made.
May also said that Trump advised her not to walk away from negotiations altogether, a piece of counsel she does agree with. Don't walk away from the negotiations.
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. "The chance to become a credible trading partner will be compromised and we will be unable to strike free-trade deals".
Tory Brexiteer Jacob Rees-Mogg called it a "bad deal for Britain".
He told the BBC's Sunday Politics: "The government unfortunately believes that Brexit is not a good thing in itself, it seems to think it has to be tempered by non-Brexit".
Boys rescued from Thai cave to be discharged from hospital next week
The Thai authorities have promised to look into the issue and fast-track applications for those who were trapped in the cave. They planned to be in the cave for an hour, but flood waters forced them deeper into the cave until they were stranded.
"Actually, no", she said.
"We agreed we need to bring Baby Trump to Bedminster", the fundraising page says, referring to the location of the Trump National Golf Club, where the president and his family often spend weekends in the summer.
"This jeopardises the opportunities offered by Brexit", Davis wrote in the Financial Times on Sunday.
Mr Baker said ministers and officials had been working for weeks on a White Paper that would have put the United Kingdom on a "different course" to the plan outlined at Chequers.
Trump called May "a very tough, very smart, very capable person", adding that he would "much rather have her as my friend than my enemy". "But we should also prepare for no deal".
Mrs May has repeatedly said Brexit will happen and has ruled out a rerun of the 2016 referendum, although French President Emmanuel Macron and billionaire investor George Soros have suggested that Britain could still change its mind.
The meeting took place in the wake of an explosive newspaper interview in which he said the Prime Minister's Brexit plans would kill off a trade deal with America and Boris Johnson would be a "great prime minister".