The information, related to the use of laptops on aircraft, came from a partner of the US which had not given permission for it to be shared with Russia, the Washington Post reports.
President Trump received Sergei Lavrov in the Oval Office last week.
National Security Adviser H.R. McMaster dismissed the reporting as “false”.
The Trump campaign’s alleged links to Russia have dogged his presidency and are part of several investigations.
However, Donald Trump has dismissed such allegations as “fake news”.
During the election campaign, President Trump repeatedly criticized his Democratic opponent, Hillary Clinton, for how she handled sensitive material.
In a conversation with the Russian foreign minister and Russian Ambassador Sergei Kislyak in the Oval Office, the president revealed details that could lead to the exposure of a source of information, officials told the Washington Post and the New York Times.
The discussion was about an ISIS plot. President Trump reportedly went “off-script”, revealing specifics of the plot, thought to centre on the use of laptop computers on aircraft, and the city from which that threat had been detected.
The intelligence disclosed came from a US ally and was considered too sensitive to share with other US allies, the papers report.
Others present realized the mistake and scrambled to “contain the damage” by informing the CIA and the National Security Agency (NSA), the Washington Post reports.
Donald Trump’s actions would not be illegal, as the US president has the authority to declassify information.
The meeting came a day after President Trump fired FBI Director James Comey, sparking criticism that he had done so because the FBI was investigating alleged Russian ties.
National Security Adviser H.R. McMaster told reporters that the story, “as reported”, was “false”.
“The president and foreign minister reviewed a range of common threats to our two countries, including threats to civil aviation,” he said.
“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.”
In a statement, Secretary of State Rex Tillerson echoed the point that “the nature of specific threats were discussed, but they did not discuss sources, methods or military operations”.
The Washington Post, which first broke the story, said this did not amount to a denial.
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