Washington (CNN) With multiple high-profile intelligence leaks in recent weeks, the US has now managed to upset two of its closest allies by allowing the disclosure of sensitive information -- a trend that is raising concerns around potentially jeopardizing the trust of key information-sharing partners.

Just days after President Donald Trump was reported to have revealed highly sensitive, likely Israeli-shared intelligence to Russian officials in the Oval Office, the United Kingdom is voicing its frustration over leaked information coming from US sources.

Although the nature of the two leaks was very different -- with the President reportedly sharing sensitive information with a foreign power in one instance and US law enforcement sources providing information to the media in the other -- the two headline-grabbing disclosures both revealed underlying frustrations maintained by those affected.

UK Home Secretary Amber Rudd slammed US leaks on the investigation into the attack at an Ariana Grande concert in Manchester, England, as "irritating" on Wednesday after a string of details emerged from US law enforcement sources before they were released by British police or officials.

"The British police have been very clear that they want to control the flow of information in order to protect operational integrity, the element of surprise," Rudd told BBC Radio 4's "Today" program. "So it is irritating if it gets released from other sources, and I have been very clear with our friends that that should not happen again."

But asked if the leaks from US officials had compromised the ongoing investigation, Rudd said she "wouldn't go that far."

In a written statement Thursday, Trump described the leaks related to the Manchester attack as "deeply troubling."

"The leaks of sensitive information pose a grave threat to our national security," the President's statement said. "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."

On Friday, Homeland Security Secretary John Kelly said he is not worried about leaks from his own department, but understands why his counterpart in the UK is frustrated by the leaks.

Kelly also commended Trump's call for the Justice Department to launch an investigation as the "the exact right thing."

"Find out who it is," Kelly said in an interview with CBS, referring to the leaks. "It's totally unacceptable, particularly when it comes to classified information."

UK Prime Minister Theresa May said Thursday she would raise the issue of leaks to US media from the Manchester bombing investigation with Trump when the pair meet later at a NATO summit in Brussels.

"I will make clear to President Trump that intelligence that is shared between our law enforcement agencies must remain secure," she said following a cabinet-level security meeting.

Shashank Joshi, a senior research fellow at the London-based Royal United Services Institute think tank, told CNN the leaks of information from the US side seemed to be more frustrating than catastrophic to the Manchester investigation.

"A lot of the information that leaked overnight Monday was fairly mundane, about casualty figures and the method of attack, but the leaking of the suspect's name was more disruptive because it might have tipped off other suspects," he said.

Amid the scrutiny over the US handling of foreign intelligence following Trump's White House meeting with senior Russian officials, Wednesday's criticism from the UK is fueling questions about the Trump administration's ability to maintain the trust of these vital partners.

"We've got a very close intelligence and defense partnership with the UK, and that news ... suggests that we have even more close allies who are questioning whether we can be trusted with vital intelligence," Sen. Chris Coons, D-Delaware, said on Wednesday in an interview with MSNBC.

"I'm hearing real questions raised whether this administration in particular, whether President Trump, understands what it means to treat highly classified intelligence carefully and responsibly," Coons said.

The issue may stem from a lack of discipline on the part of "an administration that hasn't had to deal with these kinds of processes before, according to Gen. Mark Hertling, a military analyst for CNN.

"It may be a communications issue ... the administration is not all on the same page," said Aaron David Miller, a former adviser to Democratic and Republican secretaries of state, who added that the leaks may reflect a lack of structure within the Trump administration itself.

While the UK opted to voice its frustration, Israeli officials have refrained from publicly criticizing the US in the wake of reports that Israeli intelligence was a source for some of the highly sensitive information about ISIS bomb-making capabilities that Trump reportedly discussed with Russian diplomats in the Oval Office.

Trump traveled to Israel just days after news of the Oval Office conversation broke and was greeted warmly by Prime Minister Benjamin Netanyahu, who showed no indication that Trump's interaction with the Russians posed a problem between the two nations.

It was actually Trump himself who broached the topic during an appearance alongside Netanyahu, telling reporters he "never mentioned the word or the name 'Israel'" while talking with the Russians -- a claim that was never made in the original story written by The Washington Post nor any of the follow-up reports.

"On the political level, had Trump not raised the issue in the pool spray, I don't think it would have come up," said Miller, a former political adviser who now works at the Wilson Center in Washington.

Last week, Israeli Defense Minister Avigdor Lieberman insisted there would be no effect on the close relations between the United States and Israel due to the apparent leak. But in an interview with Israel's Army Radio on Wednesday, Lieberman indicated that had carried out an internal "pinpoint correction" after reviewing the episode.

No additional details about the "correction" were provided, but Lieberman said the matter was resolved.

"Everything that needed to be clarified with the friends in the US was done,'' he said. "All of the conclusions we had to draw -- it was all done.''

But some experts say the tempered public response from Israeli politicians may be covering a deeper feeling of malcontent within the country's intelligence agencies.

"The intel community is probably beside themselves and worried about what they can confide now, if the President is going to be as careless as he was," Miller said.

Danny Yatom, who led Israel's secretive Mossad agency from 1996-98, warned that it would be a "very bad development" and a possible "catastrophe" if Trump compromised an Israeli source during the White House meeting.

"If we will assess that our sources of intelligence are in danger due to the way it will be handled by the United States, then we will have to keep the very sensitive information close to our chests," Yatom told CNN last week.

Neither the US nor Israel has acknowledged whether an Israeli source was compromised.

The US cooperates more closely with the UK and Israel on intelligence sharing than just about any other nation and repeated leaks or gaffes of this nature could have significant national security consequences, several former intelligence officials warned.

"It eliminates trust between nations, and that's the coin of the realm in terms of doing things for the betterment of the nation," Hertling told CNN. "You are not going to have the best capabilities to defend the nation if other countries aren't going to share as much with you."

According to Hertling, the most damaging fallout would occur if leaks continue to occur and US enemies are able to stockpile valuable intelligence.

But for now, Israel and the UK seem willing to look past what are widely seen as intelligence missteps from the Trump White House.

"That is the price, in a way, of dealing with world's most capable national security operation," Joshi said, adding that the US is "by far and away" the most significant intelligence partner for Britain.

Stern words will likely be directed to the US side, he said, but "on balance, it's probably not going to change intelligence-sharing arrangements all that much."