In response to the disclosures, British police investigating the Manchester attack took the highly unusual step of withholding information from U.S. agencies, which they say are responsible for the leaks. But by late Thursday evening, police said they had resumed intelligence sharing following "fresh assurances."
British authorities have not said that the leaks have hurt the investigation into the worst terrorist attack in Britain in more than a decade — 22 people died and 116 were injured Monday evening after a bomb exploded at the conclusion of a pop concert in Manchester.
But some commentators have suggested that publishing the name of the suspected bomber could have compromised the investigation. Withholding the name longer could have allowed authorities to track down people who may have since taken evasive action, they said.
There is also a marked difference in the relationship between the media and the secret intelligence services in the United States and Britain. Here, the culture is more closed, the spy agencies more secretive — it was not until 1986 that the government even officially recognized the existence of MI6. So when leaks such as this occur, it is a big deal.
May said Thursday morning she would "make clear" to Trump during the NATO summit that "intelligence that is shared between our law enforcement agencies must remain secure."
May later had a tete-a-tete with Trump while they were waiting for a photograph to be taken. Her spokesman said she told Trump that U.S.-British information sharing was "hugely important" but should be safeguarded.
John Lloyd, a media commentator, said the outrage should also be viewed in the context of Britain's upcoming election. "The election may account for some of the grandstanding," he said.
Without an election in the offing — Britons go to the polls June 8 — some politicians may have voiced their frustration "behind closed doors," he said.
In a statement issued amid meetings in Brussels with leaders of NATO member nations, Trump responded to British indignation by vowing to "get to the bottom of this."
"The leaks of sensitive information pose a grave threat to our national security. I am asking the Department of Justice and other relevant agencies to launch a complete review of this matter, and if appropriate, the culprit should be prosecuted to the fullest extent of the law," he said.
Earlier Thursday in Brussels, Trump twice declined to answer a reporter's questions about the leak controversy and British intelligence sharing. In a photo opportunity ahead of a meeting with French President Emmanuel Macron, Trump simply stared at his questioner and mouthed the words, "Thank you." He said the same thing when asked whether his former national security adviser, Michael Flynn, should cooperate with U.S. investigations of contacts with Russian officials.
Greater Manchester Chief Constable Ian Hopkins said in a statement Thursday that the leaks published by the New York Times have caused "much distress for families that are already suffering terribly with their loss."
British police chiefs across the country have also criticized the leaks in a highly unusual statement.
The National Police Chiefs' Council said that "unauthorized disclosure of potential evidence" in the middle of a counterterrorism investigation "undermines our investigations."
On Wednesday morning, Amber Rudd, Britain's home secretary, said the leaks in the U.S. media were "irritating" and should not happen again.
Hours later, the New York Times published detailed forensic photographs from the crime scene that showed, among other things, fragments of a blue backpack that may have contained the assailant's bomb. They also included a graphic of the area where the bomb exploded, pinpointing where the victims' bodies were found.
The New York Times on Thursday defended its reporting, saying in an emailed statement that "the images and information presented were neither graphic nor disrespectful of victims, and consistent with the common line of reporting on weapons used in horrific crimes."
"We have strict guidelines on how and in what ways we cover sensitive stories," the paper said. "Our coverage of Monday's heinous attack has been both comprehensive and responsible."
The growing frustration of British officials comes as allies are already smarting from Trump's disclosure of classified information to the Russian foreign minister and ambassador about an Islamic State threat.
"Everyone is very angry," said Raffaello Pantucci, director of International Security Studies at the Royal United Services Institute, a London-based think tank.
Referring to Rudd's remarks, he said that the "Five Eyes relationship is crucial to U.K. intelligence and security, and for her to openly say how unhappy she is about this shows you how angry people are." He noted that Rudd's use of the word "irritating" should be viewed through the lens of the British fondness for understatement.
Britain and the United States are members of the "Five Eyes" group (which also includes Canada, Australia and New Zealand) that allows close intelligence sharing.
But the overall transatlantic intelligence-sharing relationship will endure, he said, "because they need each other — the links are far too tight to be broken."
At a lower level, however, there could be an erosion of trust. "If I'm a cop in Manchester, I may first think, 'Do I want this to go to everybody?' if I'm wanting operational integrity," Pantucci said.
This is not the first time that operational details in an ongoing investigation have come out in the United States.
Days after the London transit bombings in 2005, for instance, images of bomb components and the inside of a subway car were leaked in U.S. media.
Andy Burnham, the mayor of Greater Manchester, said he complained to acting U.S. ambassador Lewis Lukens that the leaks were undermining the investigation.
"These leaks are completely unacceptable and must stop immediately," he said. "This behavior is arrogant and is undermining the investigation into the horrific attack on the city of Manchester."
Lukens also condemned the leaks, telling the BBC that the messages coming out of Britain were "loud and clear."
In Washington, Attorney General Jeff Sessions said in a statement that he shares Trump's "deep concern" and has talked to the British home secretary about the matter. "These leaks cannot be tolerated, and we will make every effort to put an end to it," he said. "We have already initiated appropriate steps to address these rampant leaks that undermine our national security."
William Branigin in Washington contributed to this report.