Mr Stoltenberg said the president had injected a "new sense of urgency" into the discussions on "burden-sharing".
The diplomatic faux pas set up a series of friendly yet strained interactions on Friday.
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.
During Friday's news conference with May, Trump dismissed critics of the meeting, characterizing it as deliberations that led to positive results, including every member vowing to allocate more money for defense. "I don't think you'll have any, 'Gee, I did it, I did it, you got me.' There won't be a Perry Mason here I don't think", Trump said.
May told reporters the two would be discussing "our special relationship, which is great between the U.K. and the United States".
The London mayor said he was unsure why the US President was "singling him out".
"The deal she is striking is a much different deal than the one the people voted on".
Just hours before his first official visit to the UK, Mr Trump warned the soft-Brexit deal thrashed out by Mrs May could kill a major trade relationship with the USA, claiming he would "absolutely" be prepared to walk away if it went ahead.
President Donald Trump said Thursday the U.S.is now "very, very happy" because North Atlantic Treaty Organisation allies have pledged to increase defense spending to levels "never seen before".
NATO, a pillar of the global order, emerged from a two-day confrontation with President Donald Trump on Thursday intact but distracted and shaken, a further challenge to the alliance as it faces an expansionist Russian Federation and growing authoritarianism among some of its own members.
For supporters, Trump and Brexit offer the prospect of breaking free from what they see as obsolete institutions and rules. The Trumps appeared to enjoy themselves so much that they stayed longer than scheduled.
"He's been very nice to me the times I've met him".
Mr Trump has long complained that European countries do not spend enough on their own defence, leaving the United States to shoulder an unfair burden for protecting the continent.
The New York Times ran a website headline saying: "With May's Government Teetering, Trump Gives It a Shove".
In an apparent swipe at Trump, he added: "Sometimes the corridors, comments and tweets take on more importance than what is negotiated, said or endorsed by heads of state". The White House press secretary, Sarah Sanders, insisted the president "likes and respects Prime Minister May very much". "She's got a great and handsome grace about her". "Bring a friend, if you have one", the socialist playwright penned in a note to the conservative prime minister.
As for her not taking his advice on Brexit negotiations, Trump said it was merely a suggestion.
Trump and his wife, Melania, met British Prime Minister Theresa May and her husband Philip for a formal dinner at Blenheim Palace in Oxfordshire on Thursday.
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