By Maegan Vazquez, Sarah Westwood and Boris Sanchez, CNN

(CNN) -- Conservative political provocateur Roger Stone met in May 2016 with a Russian who offered damaging information about Hillary Clinton in exchange for $2 million, Stone and former Trump campaign communications official Michael Caputo told CNN on Sunday.

The meeting was first reported by The Washington Post.

Stone and Caputo say the meeting was part of a larger effort by law enforcement to set up the Trump campaign, citing records suggesting that the man Stone met with is a Russian national who has claimed to be an FBI informant.

In letters to House Intelligence Committee Chairman Devin Nunes obtained by CNN, lawyers for Caputo and Stone say Caputo arranged a meeting between Stone and the Russian man who called himself Henry Greenberg.

Caputo's lawyer writes that his client facilitated the meeting through his Russian business partner. Greenberg told Caputo he "had information about Hillary Clinton he wanted to provide to the Trump campaign," the letter says.

Caputo and Stone did not disclose the meeting to congressional investigators, but it has become a focus in special counsel Robert Mueller's investigation into the Trump campaign, according to the Post.

In the letters to Nunes, the two political operatives assert that they were transparent in their testimony before the committee, despite not disclosing the meeting with Greenberg.

Caputo told CNN he communicated with Greenberg by phone, and while he recognized that Greenberg had an accent, Caputo "assumed he was a US citizen."

"It was May 2016," Caputo added. "Nobody was talking about Russia, collusion, etc."

Caputo said he now believes the Russian who met with Stone was an FBI informant because "the OSC (Office of Special Counsel) knew more about it than I did." He added that it was not until prosecutors informed him that Greenberg was Russian that he learned the man he had spoken with in 2016 was not a US citizen.

"I was under the understanding that he was an American citizen of Russian descent," Caputo said. "I had no reason to believe that, I just assumed it."

The letter from Caputo's lawyer states that during his testimony with the House Intelligence committee, he "answered all questions with candor and to the best of his recollection."

However, Caputo's lawyer wrote that during his interview with the special counsel, which took place more than a month ago, "his recollection was refreshed regarding one brief interaction with a Russian national in May of 2016."

"In the course of his interview with the House Permanent Select Committee on Intelligence, this specific contact was not discussed since at the time of this interview, Mr. Caputo had simply forgotten about this brief encounter in 2016," the letter states.

Caputo's lawyer relayed that he would be willing to brief the committee on the matter.

In his letter to Nunes, Stone's lawyer similarly called the testimony "entirely truthful," adding that Stone "feels obligated" to disclose the meeting because of "information brought to his attention after his appearance."

The letter states Greenberg approached Stone "wearing a Trump MAGA hat and T-shirt and spoke with what was possibly a Russian accent."

"Prior to meeting, Mr. Stone did not know anything about Mr. Greenberg, including his background or nationality. At the meeting, Mr. Greenberg proudly showed Mr. Stone photos of Mr. Greenberg and friends at several South Florida Trump rallies," the letter states.

Stone's lawyer described the encounter as a "one-time, 20-minute interaction" and stated that Greenberg offered Stone the "non-specific, damaging Clinton information" in exchange for a $2 million payment from Trump, but that Stone declined.

Stone told CNN he was disclosing the meeting now because "Mr. Caputo only brought this to my attention recently."

He also said he never discussed the meeting with the Trump campaign, nor anyone else, adding that it was "so ludicrous that I forgot about it."

California Rep. Adam Schiff, the top Democrat on the House Intelligence Committee, said Stone's testimony "appears inaccurate or deliberately misleading" and that the offer to Caputo "could not plausibly have escaped his recollection." Schiff called for the committee to provide the special counsel investigation with transcripts of their interviews and knocked the Republicans who control the panel.

"The truthfulness of many of our witnesses has been difficult to ascertain, which is why I have urged the committee to make the transcripts available to special counsel Mueller for a determination whether any witnesses committed perjury before our committee," Schiff said. "The majority's unwillingness to do so demonstrates that protecting the President remains its paramount objective, even when it means shielding witnesses who may have testified before us untruthfully."

President Donald Trump's lawyer, Rudy Giuliani, told CNN's "State of the Union" on Sunday that he doubts Trump knew about Stone's meeting.

"I doubt it. I certainly didn't know about it. It's news to me," he said.

Greenberg, who the Post said sometimes went by the name Henry Oknyansky, had difficulties with the American immigration system, and spent two years in the custody of immigration services before returning to Russia. In 2015 court filings related to his immigration status cited by Stone and Caputo, Greenberg claimed that he worked as an FBI informant for 17 years.

However, Greenberg denied he was acting on the FBI's behalf when he met with Stone, according to the Post, and the court filing the newspaper obtained said his work with the FBI halted sometime after 2013.

The letters from the two political operatives' lawyers mention a text exchange after the meeting with Greenberg and say Stone's impression was that the meetup had been a waste of time and he viewed Greenberg as "a nut."

The exchange was obtained and published by the Post.

"How crazy is the Russian?" Caputo asked.

"Wants big &$ for the info- waste of time," Stone replied.

Caputo then texted, "The Russian way. Anything at all interesting?"

"No," Stone said.

An FBI spokeswoman and a spokesman for Mueller's office declined to comment to the Post.

The meeting with Stone reportedly took place a few weeks after former Trump campaign foreign policy adviser George Papadopoulos was told about Russian dirt on Hillary Clinton and two weeks before senior members of the Trump campaign met with Russian nationals -- including a lawyer with ties to the Kremlin -- in Trump Tower.

Greenberg initially denied Stone's account of the meeting but later changed his story, giving the Post a brief description of the meeting that matched Stone's depiction in part.

While Stone told the Post that Greenberg was alone for the meeting, Greenberg relayed that he was accompanied by a Ukrainian man only identified as Alexei. Greenberg told the Post that Alexei was fired from the Clinton Foundation. He also denied he asked for money, saying played a limited role in the meeting and left it to Alexei to talk with Stone while he sat at a nearby table.

Stone told CNN he had never heard of Alexei, nor was this person present at the meeting.

The Clinton Foundation also told the Post that they had never hired someone with the first name Alexei.

A news release from Caputo following the Post story states that in his meeting with the Special Counsel's Office, he "noted the Mueller team knew far more than he did about the Greenberg approach."

After his meeting with Mueller, Caputo investigated Greenberg, the release said, and he put the information he found into a dossier online.

The disclosure of the meeting comes a month after multiple reports that the FBI dispatched a confidential source to speak with at least two advisers to Trump's presidential campaign after the bureau obtained evidence that the aides had ties to Russia. The revelations have prompted Trump to accuse the FBI of spying on his campaign and trying to frame him.