Speaking at a press conference in Sochi, Russia, Putin said the transcript could be provided if the White House agreed.
The Trump administration has come under fire over a meeting at the Oval Office with Lavrov and Russian Ambassador Sergey Kislyak last week, in which he shared security information that two sources described to CNN as classified.
The Washington Post first reported the allegations on Monday, claiming Trump had shared highly classified information in the talks.
Putin denied reports that Trump shared intelligence in the meeting, describing the media reports on the issue as “political Schizophrenia.”
“We are prepared to go there and explain our point of view to Congress if necessary,” he said.
In two tweets on Tuesday, Trump confirmed he had spoken to the Russian officials about terrorism and airline flight safety, but he did not confirm or deny whether the information was classified.
He defended his actions, saying it was his right as president to share information on security as he saw fit. The Post reported an official with knowledge of the meeting described Trump as saying: “I get great intel. I have people brief me on great intel every day,” just before revealing the intelligence.
In April, CNN first reported that US intelligence and law enforcement agencies believed that ISIS and other terrorist organizations had developed new ways to place explosives in laptops and other electronic devices to evade airport security screening methods.
Officials told CNN at the time that the ban came about following the collection of intercepted material and “human intelligence.”
According to US and diplomatic officials, Israeli intelligence was a source for some of the information about ISIS bomb-making capabilities that the President discussed with Russian diplomats.
Trump’s meeting with Lavrov and Kislyak came as the White House deals with a series of scandals linking members of Trump’s team with Russia. The FBI has confirmed it is investigating these links.
The White House has scrambled to respond to the intelligence scandal, at first denying the story, then arguing that it was “wholly appropriate” for Trump to discuss the information with the Russians.
“At no time were intelligence sources or methods discussed and the President did not disclose any military operations that weren’t already publicly known,” Trump’s national security adviser H.R. McMaster told reporters Monday night.
“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.”