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House Intelligence Committee ranking member Devin Nunes, R-Calif., told "The Story" Monday that Republicans have not referred either former President Barack Obama or former Vice President Joe Biden for criminal investigation due to their role in the Russia investigation.

"We've been running our own investigation, House Republicans have, for three and a half years and we've made our own criminal referrals," Nunes told host Martha MacCallum after Attorney General William Barr said he does not expect Connecticut U.S. Attorney John Durham’s review of the origins of the Russia probe will lead to a “criminal investigation” of either man.

"I don't want to get into who we've specifically criminally referred," Nunes went on. "So I don't want to play this cat and mouse game, so to speak. But I can tell you that we have not referred either Biden or Obama."

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"It's about what what's on the books and what law was broke," Nunes added. "You know, we may wish that some people could serve some time because they maybe knew things that were happening that were not right. But that doesn't mean they broke the law."

Earlier Monday, Barr spoke at length about the Durham investigation, saying he has a “general idea” of how the investigation is going and confirmed that “some aspects are being investigated as potential crimes.”

Barr added that “not every abuse of power, no matter how outrageous, is necessarily a federal crime.”

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MacCallum also asked Nunes to elaborate on other examples of "unmasking" of people affiliated with the Trump campaign in addition to the case of national security adviser designate Michael Flynn.

"Just through a quick cursory look ... we noticed dozens of reports that if it said 'Trump' or 'Trump transition official,' those were being unmasked. And so, you know, this is not really anything new that we haven't talked about in the past," Nunes said. "It's just that it was covered up by the media.

"That's really the problem here. You know, I went out and publicly said this, and my reward for that was being accused of leaking information to the White House."

Fox News' Brooke Singman contributed to this report.