Kremlin offer comes amid row over US president’s disclosure of ISIL-related information to top Russian diplomats.
Vladimir Putin has said that his government could provide a recording of the exchange between Sergey Lavrov, Russia’s foreign minister, and Donald Trump that has stirred up a political storm in the capital.
The Russian president’s comments on Wednesday were the first since accusations first surfaced that the US president shared secrets while meeting Lavrov at the White House.
The Washington Post newspaper has reported that Trump shared intelligence with Lavrov regarding an ISIL threat related to the use of laptop computers on airplanes.
The controversy comes amid existing investigations into whether Trump’s aides colluded with Russia during the election campaign.
Putin said he was pleased with Lavrov’s visit to the US capital last week but mocked the idea that Trump had shared secrets during the meeting on May 10, calling the allegations "political schizophrenia" and saying people spreading them are either "dumb" or "corrupt".
"We can see that political schizophrenia is developing in the United States," Putin said after talks with Paolo Gentiloni, Italian prime minister, in the southern Russian city of Sochi on Wednesday.
"I cannot otherwise explain the accusations of the president that he handed Lavrov some sort of secrets."
"If the US administration finds it possible, we are ready to provide a recording of the conversation between Lavrov and Trump to the US Congress and Senate."
Al Jazeera’s Rory Challands, reporting from Moscow, said: "It’s basically power projecting from Putin.
"He is projecting it to Donald Trump, the US Congress and the wider politial establishment there. Vladimir Putin is having a lot of fun at the moment."
Putin used the Russian word for audio recording at the press conference, but Yuri Ushakov, his foreign policy aide, said that "audio is not made" at meetings like the one at the Oval Office.
"There is a recording kept by a special person present at conversations," Ushakov clarified to Russian news agencies.
Meanwhile, in Washington, DC, "Democrats are calling on Republicans to join them in calling for an independent investigation", said Al Jazeera’s Kimberly Halkett, reporting from Washington, DC.
For Democrats but also for some moderate Republicans, there is growing concern that the Trump White House refused to hand over transcripts or tapes, with "three separate congressional investigations ongoing into Russian meddlings or ties between Russian officials and Trump’s staff", she said.
According to sources cited in the report, that intelligence that Trump reportedly leaked came from a US ally which had not authorised the US to pass it on to Russia.
The New York Times reported later that Israel was the source that shared with US spy agencies the sensitive intelligence materials.
A US administration official confirmed to AFP news agency on condition of anonymity that the original intelligence came from Israel.
However, HR McMaster, Trump’s national security adviser, denied that Trump caused any security lapses.
Trump himself insisted he had the "absolute right" to share "facts pertaining to terrorism and airline flight safety" with Russia.