British police stopped sharing information about the suicide bombing with the United States, a British counter-terrorism source told Reuters earlier, after police chiefs said the leaks to media risked hindering their investigation.
Police are hunting for a possible bomb-maker after the 22-year-old attacker, British-born Salman Abedi, detonated a sophisticated device at a concert venue packed with children on Monday night, killing 22 people.
May said she would talk to Trump at a NATO summit later on Thursday about the leaks, which included the publication of photographs of the bomb site by the New York Times.
"I will make clear to President Trump that intelligence that is shared between our law enforcement agencies must remain secure," she said in a televised statement.
The decision to stop sharing police information with US agencies was an extraordinary step as Britain sees the United States as its closest ally on security and intelligence.
"This is until such time as we have assurances that no further unauthorised disclosures will occur," said the counter-terrorism source, who spoke on condition of anonymity.
Many European cities, including Paris, Berlin and Brussels, have suffered attacks in the last two years, underlining the importance of confidential intelligence cooperation.
Trump was widely criticised this month after it emerged he had discussed sensitive Syria-related intelligence, originating from an ally, with Russian officials at a White House meeting. May said at the time Britain would continue to share intelligence with Washington.
The official threat level in Britain was raised after the Manchester attack to "critical", its highest level, meaning a further attack could be imminent. Troops have been deployed to free up police officers for patrols and investigations.
England's National Health Service said a total of 116 had been injured in the attack, with 75 admitted to hospital. Twenty-three remained under close care.
Soldiers and bomb disposal experts rushed to a street in the south of the city after a call to police, but it turned out to be a false alarm.
Queen Elizabeth visited the Royal Manchester Children's Hospital, where some of the casualties have been treated. A minute's silence was observed in honour of the victims at a square in central Manchester and in other places in Britain.
The bombing, which took place at the Manchester Arena indoor venue just after the end of a concert by U.S. pop singer Ariana Grande, was the deadliest in Britain since July 2005, when 52 people were killed in attacks on London's transport network.
The Manchester attack has caused revulsion across the world because it targeted children and teenagers, who make up the bulk of Grande's fan base. The victims range from an eight-year-old schoolgirl to parents who had come to pick up their children.
A total of eight people are in custody in connection with the attack. British media have reported that one of them is Abedi's brother but police have not confirmed that.
Manchester's police chief said on Wednesday Abedi was part of a network, and media have reported that authorities suspect he received help constructing the bomb and planning the attack.
Police chiefs have made clear they are furious about the publication of confidential material in US media, including bomb site photographs in the New York Times, saying such leaks undermined relationships with trusted security allies.
"This damage is even greater when it involves unauthorised disclosure of potential evidence in the middle of a major counter-terrorism investigation," a National Counter Terrorism Policing spokesman said in a statement.
Britain routinely shares intelligence with the United States bilaterally, and also as part of the "Five Eyes" network which also includes Australia, Canada and New Zealand.
Crime scene pictures
The pictures published by the New York Times included remains of the bomb and of the rucksack carried by the suicide bomber, and showed blood stains amid the wreckage.
"I think it's pretty disgusting," said Scott Lightfoot, a Manchester resident, speaking outside a train station in the city. He criticised media for publishing such material.
"Who's leaking it? Where's it coming from? This is British intelligence at the end of the day, people shouldn't be finding out about this."
The Financial Times reported that such images are available across a restricted-access encrypted special international database used by government ordnance and explosives experts in about 20 countries allied with Britain. It said the database was built around a longstanding U.S.-British system.
The BBC said Manchester police hoped to resume normal intelligence relationships soon but were furious about the leaks.
US channel ABC News reported that police had found a kind of bomb-making workshop in Abedi's home and he had apparently stockpiled enough chemicals to make additional bombs.
British news website The Independent also reported bomb-making materials which could be primed for imminent attacks had been found in the raids following the Manchester bombing. The report said one suspect device was blown up in a controlled explosion.
Britain routinely shares intelligence with the United States, and also as part of the "Five Eyes" network which also includes Australia, Canada and New Zealand. International cooperation.
(Additional reporting by Kate Holton, Alistair Smout, William James, William Schomberg and Paul Sandle; Writing by Estelle Shirbon and Guy Faulconbridge; Editing by Ralph Boulton)
(Except for the headline, this story has not been edited by NDTV staff and is published from a syndicated feed.)