Washington (CNN) Two former top FBI officials deny former Overstock CEO Patrick Byrne's claim that the FBI directed him in the summer before the 2016 election to pursue a "romantic relationship with Maria Butina," the Russian woman who was accused of seeking to win influence in powerful Republican circles at the behest of her country's government.

The claim was made in a live, 30-minute -- and at times bizarre -- interview on CNN Thursday, the same day that Byrne resigned from his company . He quit days after issuing a press release invoking claims of a "deep state," ​which prompted a steep stock market fall. News of his resignation saw a rebound.

Byrne's story, as told to CNN anchor Chris Cuomo on "Cuomo Prime Time," and in earlier interviews broadcast on Fox Business News and Fox News, also includes allegations that top officials in the Obama administration, including James Comey, the former FBI director, approved of the bureau's requests of him.

It has not been verified by the agencies, and spokespeople for the Justice Department and FBI declined to comment. Reached Thursday evening by CNN, Comey called Byrne's claim "ridiculous."

"The FBI doesn't work that way," Comey said.

Former FBI deputy director and CNN contributor Andrew McCabe said he hadn't heard of Byrne until the former CEO revealed his relationship with Butina.

"His allegation that his potential cooperation with the FBI was somehow discussed at the highest levels certainly never happened when I was there," McCabe, who held the No. 2 role at the agency beginning in 2016 until his firing in 2018, said Friday on CNN's "New Day."

McCabe said it was "certainly possible" that Byrne volunteered information about Butina to the FBI, but disputed the claim that agents would have told Byrne to "engage in a romantic relationship with a suspected Russian intelligence agent."

"That is simply not the sort of thing that the FBI does," McCabe said.

A US official told CNN on Thursday that Byrne met earlier this year with Justice Department officials and shared with them similar information about a romantic relationship with Butina encouraged by the FBI. The US official said that the Justice Department officials Byrne met with found aspects of Byrne's story to be believable in part because he shared operational details that were not widely known.

Byrne said he first met Butina at an event in Las Vegas in 2015. Butina, a firearms enthusiast, had spoken to him about guns, he said, and later invited him to Russia, where she had claimed to have high-powered connections.

Byrne said he then informed the FBI about her outreach to him. He had built a relationship with the FBI after helping the bureau in two previous cases, he said, adding that agents had told him he had a "non-standard relationship with the government."

The FBI, according to Byrne, greenlit and "encouraged" him to build a relationship with Butina, which he did -- saying he would be meeting with the young grad student every six weeks and discussing philosophy and politics with her.

Byrne said he grew concerned as Butina mentioned her relationship with Kremlin-linked banker Alexander Torshin, who she said had directed her to try to build inroads into the upper reaches of American politics. Butina's efforts in the US and her communications with Torshin have been borne out in court filings in the case brought by prosecutors in Washington, DC, against Butina last year.

Prosecutors accused Butina of trying to make inroads with prominent political groups, including the National Rifle Association, to promote Russian interests. She pleaded guilty late last year to a lesser count and admitted in a plea agreement to acting "under direction of" a Russian official whom CNN has identified as Torshin. She is currently serving an 18-month prison term . Torshin did not respond to requests for comment from CNN as the charges against Butina played out.

Byrne said he reported what he'd learned about Butina's mission in the US to the FBI, but that "they kept on dismissing it."

"It was so strange that I was thinking, it's almost like they're letting this can-o-scandal develop and someday they're going to shake it up and crack it and spray it all over the Republican Party," he said.

Byrne later claimed the FBI told him to break off his relationship with Butina, before approaching him again in July of 2016, saying he needed to "rekindle" his relationship with her to assist the bureau's efforts during a time it was investigating attempts by Russia to interfere in the US presidential election.

"They came back to me and said, 'Boy, what a mistake we made. Russia, you're right ... highest national priority,' " he said.

"They said, 'We want to be clear -- this never happens in the United States,' " Byrne added. " 'We are the good guys, we don't work like the bad guys, but we need to ask you to rekindle a romantic relationship with Maria Butina.' "

Asha Rangappa, a former FBI official and CNN legal analyst, said elements of Byrne's claims about how the FBI encouraged his initial efforts to build a relationship with Butina line up with how the bureau would typically run a counterintelligence investigation.

But she said she was skeptical about his claim that the bureau later encouraged him to have a "romantic relationship" with Butina.

"If he had a romantic affair with her on his own, and was providing information to them, I don't know that that would necessarily be out of the bounds," she said. But if the FBI had asked him to have a romantic relationship, "that to me seems incredibly suspect only because there is a lot of legal liability that's involved with that. You can imagine the he said/she said situations," she said.

Byrne's comments and resignation as CEO of Overstock come after he published a press release earlier this month claiming that he helped the FBI carry out "political espionage."

"Coming forward publicly about my involvement in other matters was hardly my first choice," Byrne wrote in the letter about his resignation. "I now plan on leaving things to the esteemed Department of Justice (which I have doubtless already angered enough by going public) and disappearing for some time."

Earlier this year, Attorney General William Barr tasked the top federal prosecutor in Connecticut, John Durham, with reviewing the way the intelligence community operated in the early days of the Russia investigation. It is not clear if Byrne's claims have been scrutinized by Durham.

Butina's attorney, Robert Driscoll, said of Byrne's resignation, "I wish him well. I think he raised issues worthy of investigation, at risk to his career, as has become apparent."

This story has been updated.