Washington(CNN) President Donald Trump was infuriated after it quickly leaked that he had been directly instructed by his national security advisers in briefing materials not to congratulate Russian President Vladimir Putin on his recent election victory during their call Tuesday morning, a source familiar with the President's thinking said.

Trump was fuming Tuesday night, asking his allies and outside advisers who they thought had leaked the information, noting that only a small group of staffers have access to those materials and would have known what guidance was included for the Putin call, the source said.

According to the source, the incident resurfaces his long-held belief there are individuals inside his administration -- especially in the national security realm -- who are actively working to undermine him.

White House chief of staff John Kelly also is furious that a confidential presidential briefing became public knowledge, a White House official said, and intends to address the matter Wednesday as aides try to figure out who disclosed the warning.

"If this story is accurate, that means someone leaked the President's briefing papers. Leaking such information is a fireable offense and likely illegal," another senior White House official told CNN Wednesday.

The Washington Post first reported Tuesday that Trump congratulated Putin despite warnings from multiple national security advisers and briefing materials that said "DO NOT CONGRATULATE." The White House declined to officially comment to CNN on the matter, with an official adding that they "cannot comment on alleged classified deliberative documents allegedly provided to the President."

The President often makes calls to foreign leaders while he is still in the residence during what has been dubbed "executive time." National security adviser H.R. McMaster has been known to join Trump in the residence during these calls, and was present during his Tuesday morning call with Putin. According to the public schedule released by the White House Tuesday, the President was not scheduled to be in the West Wing until noon, when he greeted the Saudi crown prince.

The leak, which one source said contributes to the ongoing atmosphere of paranoia in the West Wing, irked White House aides as well. Though the reaction has been described as "rattled," a White House official said it is more like anger and disappointment.

"This is unacceptable," the White House official said, speaking about the leak that some believe was an attempt to embarrass the President and McMaster. Another called it "ridiculous."

One of the White House officials described anger and disappointment in the West Wing over the leak.

It is still unclear if Trump actually read the guidance that was given to him by his advisers. Multiple officials have noted that he often follows his own path during his calls with world leaders. The substance of the call was not seen as a major deal by national security staffers, but the leak certainly was.

Another White House official didn't dispute to CNN Tuesday the language on the notes provided by members of Trump's National Security Council, but said Trump didn't read or see the notecard. The official added that Trump often disregards advice in calls with foreign leaders.

Trump's comments drew significant criticism among US politicians, including by Arizona GOP Sen. John McCain, a noted Russia hawk, who said "an American president does not lead the free world by congratulating dictators on winning sham elections."

The leak comes as McMaster's standing in the West Wing remains in question. After Trump fired Secretary of State Rex Tillerson on Twitter last week, speculation intensified that McMaster was next to be ousted. The White House denied last week that McMaster was on his way out.