Trump also said that immigrants were destroying European culture and that he planned to maintain good relations with Russian President Vladimir Putin despite nerve agent attacks on United Kingdom soil that have been blamed on the Kremlin.
Trump accused the prime minister of ignoring his advice on Brexit negotiations, in remarks that echoed Johnson's private barbs that the United States president would do a better job than May in negotiations. The interview was published as Mrs May hosted Mr Trump and Melania for a black-tie dinner at Blenheim Palace, with the President briefly taking Mrs May's hand as they arrived in a scene reminiscent of the infamous hand-holding shortly after his election.
On Thursday, Trump told reporters at a press conference in Brussels that to him, Putin, was a "competitor" rather than an enemy.
Trump also singled out Germany and its chancellor Angela Merkel for criticism, a day after saying Berlin had become a "captive of Russia" because of a gas pipeline deal and should be paying more for defense.
"Prior to past year, where I attended my last meeting it was going down, the amount of money being spent by countries was going down and down very substantially", he said.
"The deal she is striking is a much different deal than the one the people voted on", he said. "I'm very strong on immigration".
Britons are narrowly in favour of US President Donald Trump airing his views on Brexit, a Sky Data poll suggests. "I hope you have no doubt this is an investment in our security, which can not be said with confidence about Russian & Chinese spending".
During the press conference, Mr Trump - who regularly accuses the United States media of "fake news" over its coverage of him - also clashed with a reporter from the American NBC network, describing it as "possibly worse than CNN". "I think he has done a very bad job on terrorism", he said. "I actually told Theresa May how to do it, but she didn't listen to me".
Israel announces mission to land spacecraft on the Moon
Once the mission is accomplished, the developer said the spacecraft will remain on the moon as a " symbol of Israeli success ". The Google prize expired in March without a victor having reached the moon, but Israel's team pledged to push forward.
"President Trump never at any moment, either in public or in private, threatened to withdraw from North Atlantic Treaty Organisation", he said.
But Macron disputed Trump's claims, saying that the joint statement the leaders had signed went no further than what had previously been agreed, apart from setting out how some countries plan to get there.
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". "We wanted to embarrass him and I think we have done that today".
"I think we could have a very good relationship with President Putin", Trump said, adding that he was not going into the meeting with "high expectations".
Trump said he did not criticize May during the interview and said the British tabloid did not include all the good things he said about her.
Trump blamed London mayor Sadiq Khan for allowing the protests and blasted the city's first Muslim leader as weak on terror and crime.
US-Russian relations have suffered from years of disagreement over the Syrian conflict, Russia's annexation of Crimea and its involvement in eastern Ukraine.
"I know Londoners are resolutely opposed to the politics of fear and despair".