U.S. President Donald Trump has called leaks to U.S. media about the Manchester bombing investigation "deeply troubling" and vowed to find out what happened.

Responding to British Prime Minister Theresa May's outrage over a New York Times story publishing forensic photos of the crime scene, Trump said the leaks were a "grave threat to our national security."

The Times defended its publication of the photos as part of a "comprehensive and responsible" coverage plan of the attack that followed strict guidelines.

Trump wasn't the only one troubled by the leaks about the suicide bombing, which left 22 people dead. After leaked material appeared in U.S. news reports, Britain briefly froze its intelligence-sharing with the U.S.

Damage was done, says former MI5 intelligence officer Annie Machon, but relations mended later Thursday when the U.K. reinstated intelligence sharing with U.S. after the British head of counter-terrorism policing said he's received "fresh assurances" from the Americans.

Manchester Police say 22-year-old Salman Abedi was the suicide bomber who targeted the crowded arena. (Associated Press)

Machon's main worry is not about the Times story showing pieces of the bomb and backpack, but U.S. media reports that identified the suicide bomber Salman Abedi before British authorities named him. (Abedi's name was already floating around social media at the time.)

"Other extremists feeling hunted may have taken desperate action to bring ahead another attack," she says.

Trump was "absolutely right" to call for an investigation into leaks, Machon says, due to the deluge that was beginning to "erode his authority as a new president."

But reviews into leaks can face real challenges. Here are three questions about a potential probe.

How hard is it to prosecute leak cases?

Pretty hard, says David Bitkower, a former principal deputy assistant attorney general for the Justice Department's criminal division.

"Leaking per se is not a crime unless the government can prove it violated a specific federal statute," Bitkower says. For example, if the leaked information were obtained through a grand jury, or if it involved classified information.

Britain briefly suspended its intelligence-sharing with the U.S. after leaks relating to the deadly Manchester attack where revealed in American media. Not long after, the intelligence sharing resumed. (Emilio Morenatti/Associated Press)

In the more common "classified" context, a prosecutor would generally have to show the leaker had "reason to believe" the information being passed along could harm the U.S., yet decided to leak it anyway, Bitkower says.

The hard part is proving a person's foreknowledge that the material being leaked could hurt U.S. interests. The "classified" marker is one way to characterize such sensitive documents.

Bitkower was not willing to comment on the Manchester case, but a consequence of this point is that if photos of the backpack and shrapnel from the Manchester attack were not explicitly marked "classified," it might be challenging for a prosecutor to show a leaker knew their potential — if any — for causing harm to the U.S.