The newspaper said the information Trump relayed to Russian Foreign Minister Sergey Lavrov and Russian Ambassador Sergey Kislyak had been provided by a US ally through a highly sensitive intelligence-sharing arrangement.
The ally had not given Washington permission to share the material with Moscow, and Trump's decision to do so risks cooperation from an ally that has access to the inner workings of Islamic State of Iraq and the Levant, the Post said, citing unnamed officials.
During his Oval Office meeting with Lavrov and Kislyak, Trump went off-script and began describing details about an ISIL threat related to the use of laptop computers on aircraft, the officials said.
"The officials are also quoted as saying that Trump indicated the town under ISIL control where this information was obtained, giving rise to the possibility that ISIL could learn more about collection methods of the information or even who got the information in the first place,” Al Jazeera's Mike Hanna, reporting from Washington, DC, said.
While discussing classified matters with an adversary would be illegal for most people, the president has broad authority to declassify government secrets, making it unlikely that Trump's disclosures broke the law, the Post said.
Trump's meeting with Lavrov and Kislyak at the White House came a day after he fired FBI Director James Comey, who was leading the agency's investigation into possible links between Trump's presidential campaign and Moscow.
Asked about the disclosures, Trump's national security adviser, HR McMaster, who participated in the meeting, said no intelligence sources or methods were discussed that were not already known publicly, the Post reported.
"This story is false. The president only discussed the common threats that both countries faced," said Dina Powell, deputy National Security Advisor for Strategy.
US officials have told Reuters news agency that US agencies are in the process of drawing up plans to expand a ban on passengers carrying laptop computers onto US-bound flights from several countries in conflict zones because of new intelligence about how armed groups are refining techniques for installing bombs in laptops.
So serious are assessments of the increased threat that Washington is considering banning passengers from several European countries, including Britain, from carrying laptops in a cabin on US-bound flights. The United States has consulted about the intelligence with allied governments and airlines.
According to a Reuters/Ipsos opinion poll released on Monday, a majority of Americans, including a growing number of Republicans, want to see an "independent investigation" to sort out any connections between Russia and Trump during the 2016 election campaign.
The May 10-14 poll, which was conducted after Trump fired Comey, suggests the public is increasingly uneasy with allegations of meddling by the Russians in the US election. Trump's dismissal of Comey, who was leading the FBI's probe into ties between the White House and Russia, intensified calls by Democrats for an independent probe.
According to the poll, 59 percent of adults, including 41 percent of Republicans and 79 percent of Democrats, agreed that "Congress should launch an independent investigation into communications between the Russian government and the Trump campaign during the 2016 election".