In a newspaper interview published just hours before holding talks with May, Trump said her Brexit strategy would "kill" any chance of a trade deal and said she had not listened to his advice on how to negotiate with the EU.
Downing Street has not yet reacted to Mr. Trump's remarks, the BBC reports.
The white paper produced by the UK Government represents an evolution in its position on Brexit, Irish prime minister Leo Varadkar has said.
In the interview, which took place at the U.S. Embassy in Brussels, the president also lashed out at the Muslim mayor of London, saying he had done "a awful job".
Massive protests are greeting President Trump during his two-day trip to Britain-including a 20-foot-long giant blimp depicting Trump as an angry orange baby wearing a diaper and clutching a cellphone, ready to tweet.
Trump also said he was "cracking down" on the European Union as "they have not treated the United States fairly on trading".
A few hundred people gathered to watch the blimp launch in Parliament Square, with organizers of the stunt wearing red boiler suits and red baseball caps emblazoned with "TRUMP BABYSITTER". The US looks forward to finalising a great bilateral trade agreement with the UK.
He didn't elaborate. He said that May is "doing a terrific job".
After the question was posed to the USA president, the reporter appeared to be ushered out of the room at Chequers, the official residence of the PM.
The US president apologised to Mrs May on Friday over an incendiary interview criticising her premiership, and hailed UK-US relations as the "highest level of special".
Organizer Daniel Jones, a charity communications officer aged 26, said they were trying to make people laugh as well as making a serious point.
Unlike with Prime Minister Theresa May earlier in the day and in previous meetings, Mr Trump did not attempt to hold the hand of his female host as they came down the stairs to inspect the troops. I get along with her very nicely.
They met on the dais in the castle's Quadrangle, and the United States national anthem was played on his arrival.
"I think they like me a lot in the UK", Mr Trump had said in Brussels. "I used to love London as a city".