The intelligence shared at the meeting with Russian Foreign Minister Sergei Lavrov and Russian Ambassador Sergei Kislyak was supplied by a US ally in the fight against the militant group, both officials said.
The White House said the allegations, first reported by the Washington Post, were not correct.
"The story that came out tonight as reported is false," HR McMaster, Trump's national security adviser, told reporters at the White House, adding that the two men reviewed a range of common threats including to civil aviation.
"At no time were intelligence sources or methods discussed. The president did not disclose any military operations that were not already publicly known. ... I was in the room. It didn't happen," he said.
The White House also released a statement from Secretary of State Rex Tillerson, who said the meeting focused on counterterrorism, and from deputy national security adviser Dina Powell, who said the Washington Post story was false.
Reacting to the news, the Senate's No. 2 Democrat, Dick Durbin, called Trump's conduct "dangerous" and "reckless." The Republican head of the Senate Foreign Relations Committee, Bob Corker, called the allegations "very, very troubling" if true.
The latest controversy in the White House came as it continued to reel from the fallout over Trump's abrupt firing of FBI Director James Comey last week and amid congressional calls for an independent investigation into allegations of Russian meddling in the 2016 US election.
On Monday, one of the officials said the intelligence discussed by Trump in the meeting with Lavrov was classified "Top Secret" and held in a secure "compartment" to which only a handful of intelligence officials have access.
After Trump disclosed the information, which one of the officials described as spontaneous, officials immediately called the CIA and the National Security Agency, both of which have agreements with a number of allied intelligence services, and informed them what had happened.
While the president has the authority to disclose even the most highly classified information at will, in this case he did so without consulting the ally that provided it, which threatens to jeopardize what they called a long-standing intelligence-sharing agreement, the US officials said.
Trump, a Republican who has called allegations of links between his presidential campaign and Russia a "total scam," has sharply criticized his 2016 election rival, Democrat Hillary Clinton, for her handling of classified information as secretary of state, when she used a private email server.