"Another attack in London by a loser terrorist".
Trump was accused of betraying intelligence details by saying those responsible for an explosion on an underground train "are sick and demented people who were in the sights of Scotland Yard".
"I never think it is helpful for anyone to speculate on what is an ongoing investigation", May told the BBC.
Mr Trump today also used the London train attack to renew calls for his controversial ban on travelers from several predominantly Muslim countries - a rallying cry of his right-wing base who have recently been angered by his support for an amnesty for some migrants. And we have to be very smart and we have to be very, very tough, which perhaps we're not almost tough enough.
"It's a bad thing. Perhaps we are not almost tough enough", he said. "It is a bad thing - just keeps going and going". I spoke with the British Prime Minister, Theresa May, this morning and relayed America's deepest sympathy as well as our absolute commitment to eradicating the terrorists from our planet. "We have to be tougher and we have to be smarter".
There was talk earlier this year of suspending transatlantic security briefings after details of the investigation into the bombing of an Ariana Grande concert in Manchester, northern England, which killed 22 people, were leaked to the media by U.S. authorities.More news: Disappointed Trump supporters say he's 'going soft' on border wall promise
The New York Times then published detailed photographs taken from the bomb scene which had been taken by British investigators.
The president has repeatedly criticized London Mayor Sadiq Khan, the British capital's first Muslim leader.
The "special relationship" had already come under strain earlier in the year, when the then White House press secretary Sean Spicer repeated claims that GCHQ, the United Kingdom surveillance agency, had been involved in bugging the Trump campaign on behalf of Barack Obama.
The normally tight-lipped agency called the allegations "nonsense", adding that "they are utterly ridiculous and should be ignored".
"My priority is making sure that we do what we can to keep Londoners safe".
Asked by Stephanopoulos about her comments, May replied, "It is necessary for us to look, as we are doing, at whether our police and security services have the full capabilities, the powers that they need. That's quite clear what he thinks about that".