President Donald Trump meets with Russian Ambassador Sergei Kislyak. Russian Embassy

Some of President Trump's advisers and staff are afraid to leave him alone in meetings with foreign leaders for fear he might say something untoward, The New York Times reported on Tuesday.

The Times' report comes as Trump's administration grapples with its latest controversy, in which it emerged that Trump disclosed top-secret intelligence to Russian officials during a meeting in the Oval Office last week.

That intelligence, the Times reported on Tuesday, came from Israel, a key US ally. Israel is also a primary adversary of Iran, which is one of Russia's closest allies. Trump's dissemination of the intelligence to Russians, two Israeli officials told BuzzFeed News, was "our worst fears confirmed."

The president's tendency to speak off-the-cuff, as he did during his conversation with Russian foreign minister Sergey Lavrov and Russian ambassador Sergey Kislyak, has prompted his national security adviser H.R. McMaster to "insert caveats or gentle corrections" into conversations when he thinks the president is going off on a tangent or getting into diplomatic tangles.

His staff's intervention has not been well-received by Trump, the Times noted, citing two officials with knowledge of the situation. Trump is reportedly still upset that former national security adviser Michael Flynn had to resign after it emerged that he had misled the vice president about contacts he'd had with Kislyak. McMaster, Trump reportedly said, talks too much and is "a pain."

The Times characterized White House staff as being "besieged" and still trying to contain fallout from when Trump abruptly fired FBI director James Comey — who was spearheading an investigation into the Trump campaign's ties to Russia — last week. This week's chaos has not improved the mood, especially since Trump himself has become increasingly frustrated and lashed out at his aides, calling them "incompetent," according to one adviser who was lambasted.

Following the events of last week, Trump may also be considering a massive staff shake-up.