Trump said: "The relationship between our two nations is indispensable to the cause of liberty, justice, and peace".
The diplomatic faux pas set up a series of friendly yet strained interactions on Friday.
Such public criticism by a sitting USA president of a British prime minister while on a visit to the United Kingdom publicly undermines May in her party, her country and overseas.
He also told the tabloid that he had shared advice with May during Britain's negotiations with the European Union, but said May ignored his advice.
The emergency session was called followed a morning meeting between North Atlantic Treaty Organisation leaders and the leaders of Ukraine and Georgia, amid claims Mr Trump demanded non-Nato members leave the room.
Trump described Brexit as a "very tough situation... between the borders and the entries into the countries and all of the things", saying: "The only thing I ask is that she work it out so that we can have very even trade".
A large balloon depicting the USA president as a giant infant will be allowed to fly over London during the president's four-day visit to the United Kingdom after the capital's Mayor Sadiq Khan gave his permission.
"There is no stronger alliance than that of our special relationship with the United States and there will be no alliance more important in the years ahead", the British leader said.
"We're going to discuss the real opportunity we've got on a trade deal coming, and, of course, we'll discuss the defense relationship", May said. She was hoping to win over critics of her Brexit proposal with the release of a 104-page document outlining details of the plan.
Despite a series of diplomatic spats between Britain and Trump, the British government is hoping for a quick trade deal with the U.S. after it leaves the European Union.
President Donald Trump and first lady Melania Trump are welcomed by British Prime Minister Theresa May and her husband Philip May as they arrive for a black-tie dinner with business leaders at Blenheim Palace, west of London, on Thursday.
At the same time Washington wanted to put on paper its concerns over Moscow's alleged meddling in the 2016 president election in the United States, the newspaper said, citing unnamed U.S. officials.
But if Mr. Trump was expecting a friendly reception from our allies, he was in for a big surprise. The Trumps appeared to enjoy themselves so much that they stayed longer than scheduled.
"She said: 'Don't worry it's only the press.' I thought that was very professional".
But since coming to power past year, Trump has sought to improve relations with Putin amid tensions between Moscow and the West.
The interview has overshadowed what was an important visit by Trump for May's government.
Referring to the Brexit blueprint, which was outlined by the government on Thursday, he said: "The deal she is striking is a much different deal than the one the people voted on".
THE FACTS: Trump has said this before; it's not true. The White House press secretary, Sarah Sanders, insisted the president "likes and respects Prime Minister May very much".
"She should negotiate the best way she knows how. She's got a great and attractive grace about her".