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The news report was immediately refuted by both the Secretary of State Rex Tillerson and the National Security Advisor, who said that there was no discussion of specific threats with the Russians.
"This is code-word information," an unnamed US official familiar with the matter, was quoted as saying by The Washington Post.
Code-word information is a terminology that refers to one of the highest classification levels used by American spy agencies, the daily reported.
Trump "revealed more information to the Russian ambassador than we have shared with our own allies," the newspaper said, adding that following this, US officials have gone into damage control mode.
According to the daily, the sensitive classified information was given to the US by one of its allies, which had not given it permission to share this with the Russians.
However, the Trump Administration denied the allegations.
"During President Trump's meeting with Foreign Minister Lavrov, a broad range of subjects were discussed among which were common efforts and threats regarding counter-terrorism.
During that exchange, the nature of specific threats were discussed, but they did not discuss sources, methods or military operations," Tillerson said.
"The President and the (Russian) foreign minister reviewed common threats from terrorist organisations to include threats to aviation," said HR McMaster, the National Security Adviser, who participated in the meeting.
"At no time were any intelligence sources or methods discussed and no military operations were disclosed that were not already known publicly," McMaster said.
"This story is false. The President only discussed the common threats that both countries faced," said Dina Powell, Deputy National Security Advisor for Strategy, who also attended the meeting.
But The Washington Post said the information the President relayed had been provided by a US partner through an intelligence-sharing arrangement considered so sensitive that details have been withheld from allies and tightly restricted even within the US government, officials said.
Talking to reporters, McMaster described the story as false.
"The President and the Foreign Minister reviewed a range of common threats to our two countries, including threats to civil aviation.
"At no time, at no time, were intelligence sources or methods discussed and the President did not disclose any military operations that were not already publicly known," McMaster said.
"Two other senior officials who were present, including the Secretary of State, remember the meeting the same way and have said so. Their on-the-record accounts should outweigh those of anonymous sources. I was in the room. It didn't happen. Thanks, everybody," McMaster said without taking any questions.
In a statement, the Democratic Leader Nancy Pelosi said if news reports are true, Trump has "compromised a key source of intelligence collection" against ISIS and jeopardised the security of the American people.
"Even if President Trump unwittingly blew a highly classified code-word source to the Russians, that would be dangerous enough.
"If the President outed a highly classified code-word source intentionally, that would be even more dangerous," Pelosi said.
She demanded that Congress must be given a full briefing on the extent of the damage President Trump has done in compromising highly classified code-word intelligence to the Russians.