The White House has not denied that classified information was disclosed in last Wednesday's meeting between Mr Trump and Russian diplomats.
White House officials denounced the report, saying the president did not disclose intelligence sources or methods to the Russians.
Defending Trump's actions, officials played down the importance and secrecy of the information, which had been supplied by Israel under an intelligence-sharing agreement, and Trump himself said he had "an absolute right" as president to share "facts pertaining to terrorism" and airline safety with Russian Federation.
"In the context of that discussion, what the president discussed with the foreign minister was wholly appropriate to that conversation and is consistent with the routine sharing of information between the president and any leaders with whom he is engaged".
The White House issued a furious denial near the end of a tumultuous day spent beating back potentially disastrous news reports from dawn to dusk.
The official would not say which country's intelligence was divulged. But he suggested Trump did not intend to reveal classified information because he "did not even know where that information came from".
One U.S. official said the Obama administration was particularly concerned about the handling of documents related to the government's contingency plans for crises.
Trump last week shared highly classified information with senior Russian officials during an Oval Office meeting, putting at risk a source of intelligence on the Islamic State group, according to a current USA official.
The official said the disclosure came as Trump boasted about his access to classified intelligence. An excerpt to an official transcript of the meeting reveals that Mr Trump told them, "I get great intel".
"I get great intel". The former USA officials requested anonymity in order to discuss the handling of classified information.
The extraordinary leak of Trump's private conversations in the Oval Office appeared to be a direct effect of the president's combative relationship with the US spy agencies.
When asked whether he was concerned that Trump's disclosure might discourage other USA allies from sharing sensitive intelligence with the U.S. in the future, McMaster replied, "No, I'm not concerned at all".
Sen. Collins calls Trump revelation of classified info 'very troubling'
When questioned by the press, McMaster did not answer a question about whether the information shared by Trump was secret or not. Trump reportedly shared the information during last week's White House meeting and even boasted about the intelligence he had.
As President, Mr Trump has the power to disclose classified information as he chooses. Such sharing "could be a risk for our sources", the official said.
The Washington Post report on Monday led to the latest feeding frenzy, reports AFP.
Parroting what has by now become a familiar White House talking point, McMaster said the real threat to U.S. national security was United States intelligence community leaks to the press. The official spoke on condition of anonymity because the official was not authorized to speak publicly.
Multiple media outlets, including CNN, the Wall Street Journal and the New York Times, are now reporting Israel was the source of the information.
A USA official who confirmed the disclosure to The Associated Press said the revelation potentially put the source at risk. To know that this intelligence is shared with others, without our prior knowledge?
Still, experts say the revelation could jeopardize Israel's intelligence-gathering methods, which rely largely on human intelligence sources.
There are also concerns on Capitol Hill.
"The president and the foreign minister reviewed a range of common threats to our two countries including threats to civil aviation", McMaster said.
Mark Warner of Virginia, top Democrat on the Senate intelligence committee, said he would ask Comey for additional material as part of that panel's investigation.
McMaster would not confirm whether the information Trump disclosed was classified or whether it came from a U.S. ally. Following a meeting with Turkish President Recep Tayyip Erdogan, Trump said only that his meeting last week with Russian Foreign Minister Sergey Lavrov was "very, very successful".
One official said it appeared the transition aides were moving the information from the transition offices to the White House, a distance of just a few blocks. The communications team, in particular, has come in for sharp criticism from the president, as well as his son-in-law and senior adviser Jared Kushner.
Mitch McConnell, the Republican leader of the Senate, said simply: "It would be helpful to have less drama emanating from the White House". AP writer Paisley Dodds contributed from London.
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