Speaking at a press conference in Sochi, Russia, Putin dismissed allegations that Trump had shared top-secret security intelligence with Russian diplomats as "political schizophrenia."
"If the US administration finds it necessary, we are ready to provide the record of the conversation between Trump and Lavrov to the Senate and Congress," Putin said.
The intervention by Putin could turn up the pressure on the White House to provide its own transcript of the meeting. The Senate intelligence committee has already demanded a briefing on what was said at the meeting
from members of the Trump administration who were present.
The episode is the latest woe for Trump, whose administration is engulfed in a series of scandals linked to Russia. His meeting with Lavrov and Russian Ambassador Sergey Kislyak came a day after Trump fired FBI director James Comey
, the man leading an investigation into contentious links between members of the President's campaign team and Russia.
Trump has admitted sharing security information on terrorism and aviation safety with the Russians, saying he had the "absolute right" to do so, but the White House has not confirmed or denied whether that information was classified.
The Washington Post first reported
the allegations on Monday, saying that Trump described details to Lavrov and Kislyak about how ISIS hopes to use laptop computers as bombs on planes.
It reported that 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. Two sources told CNN that the information was classified.
According to US and diplomatic officials, Israeli intelligence was a source for some of the information about ISIS bomb-making capabilities.
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."
'Dumb, dangerous, dirty'
At the press conference in Sochi, Putin made light of the allegations.
"I think we need to come up with some sort of punishment for him, because he didn't share this secret information, not with us, not with the special services. This is really not nice of him," Putin joked, laughing with Lavrov, who was also at the conference.
But he then took a more serious tone, accusing Americans of "rocking the internal political situation in the US under anti-Russian slogans."
"They either don't understand that they are harming their country -- which makes them just dumb -- or they understand, which makes them dangerous and dirty."