The related information-sharing arrangement was considered so sensitive that details have been withheld from allies and tightly restricted even within the USA government, according to the Post report.
"We have no way to know what was said, but protecting our nation's secrets is paramount", said Mr Doug Andres, a spokesman for Republican House Speaker Paul Ryan, adding that the latter hopes "for a full explanation".
Trump declared on Twitter Tuesday that it was his "absolute right" to share information with other countries.
The revelations could further damage Trump's already fraught relationship with USA intelligence agencies.
"We don't say what's classified, what's not classified".
The official said the information Mr Trump divulged came from a USA intelligence partner. "I think national security is put at risk by this leak and leaks like this", he said.
Still, the weaker dollar is likely being more heavily affected by disappointing economic data, with the New York Fed manufacturing data falling into negative territory for the first time since Trump's election.
Ron Dermer, the country's ambassador to the US, said in a statement that "Israel has full confidence in our intelligence-sharing relationship with the United States and looks forward to deepening that relationship in the years ahead under President Trump". During a stop in Saudi Arabia, he'll meet with important Arab allies working with the USA on the fight against the Islamic State.
Senate Majority Leader Mitch McConnell paused and answered simply "no" when asked if he had concerns about the president's ability to properly handle classified information in wake of the revelations.
Responding to McMaster's defense, Dan Pfeiffer, a former top official in Barack Obama's White House, wrote, "You can not overstate how unprepared and ill-suited Trump is for the presidency and how poorly his White House is run".
Global network to continue sharing info with United States despite secrets leak.
Trump tweets that 'perfect accuracy' is not possible for his 'surrogates'
Trump also denied reports that he asked Comey to pledge his loyalty to him at a private dinner shortly after Trump was sworn in. Trump emphasized that Flynn had done nothing wrong, reportedly telling Comey, "He is a good guy".
USA allies including Australia, New Zealand and Japan cited the White House denials and said intelligence sharing would continue. "Our fight is against ISIS", Trump said.
But then Trump seemingly admitted sharing information, tweeting Tuesday: "As President I wanted to share with Russian Federation. which I have the absolute right to do".
Trump's acknowledgement that he had given sensitive information during a White House meeting last week undercut intense efforts by senior aides to play down the incident on Monday evening, after news reports emerged of Trump's conversations about a planned Islamic State operation.
The disclosure also risks harming his credibility with USA partners around the world ahead of his first overseas trip.
While Trump continues to dismiss as "fake news" investigations of Russian meddling and whether any of his associates colluded in it, the FBI and committees in Congress are pressing ahead with probes.
White House denies Trump disclosed intelligence.
"The premise of that article is false, that in any way the president had a conversation that was inappropriate or that resulted in any kind of lapse in national security", McMaster said at the White House.
The US also maintains open intelligence-sharing relationships with allies like France, Germany and Japan.
American presidents have the power to unilaterally disclose any material - even the most secret intelligence - without going through any kind of formal process, or worrying about prosecution.
This morning, Trump tweeted that he did share intelligence, but that he was allowed to, and needed to. In his research, Priess, who interviewed several former presidents, said he "did not get any sense" that presidents on "an ad-hoc basis simply decide to disclose code-word" - very sensitive - information. "I'm leaving. I'm leaving", he said when questioned by reporters.
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