House Oversight Committee Chairman Jason Chaffetz Jason ChaffetzThe myth of the conservative bestseller Elijah Cummings, Democratic chairman and powerful Trump critic, dies at 68 House Oversight panel demands DeVos turn over personal email records MORE (R-Utah) on Friday questioned former national security adviser Michael Flynn's offer to speak to congressional investigators if granted legal immunity, calling the proposal "very mysterious."

In an interview with Fox News, Chaffetz also chided President Trump's Friday morning tweet in which he defended Flynn's request for immunity and called congressional investigations into his potential ties to Russia a "witch hunt."

"No, I don’t think it’s a witch hunt,” Chaffetz said in the interview. "Look, it’s very mysterious to me, though, why all of a sudden General Flynn is suddenly out there saying he wants immunity.

"I don’t think Congress should give him immunity. If there’s an open investigation by the FBI, that should not happen. I also don’t believe that, actually, that the president should be weighing in on this," he continued. "They’re the ones that actually would prosecute something."

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Flynn's attorney, Robert Kelner, said Thursday that the former Trump aide was willing to be interviewed by members of the House and Senate Intelligence committees as part of their investigations into Russia's meddling in the U.S. presidential election and potential ties between Trump's associates and the Kremlin. But that interview would only come only if Flynn was guaranteed immunity from prosecution, he said.

"Immunity for what?" Chaffetz said. "I mean, we don't know what that is. And so it's up to the Intelligence Committee — I'm on the Oversight Committee. But sitting in Congress, having been through this. You use that very sparingly."

Flynn resigned from his post in February amid revelations that he discussed sanctions with Russia's ambassador before Trump took office. Flynn stirred controversy again this month after registering as a foreign agent and revealing that he had done lobbying work that may have benefited the Turkish government.

While requests for legal immunity are not admissions of guilt, Chaffetz said, that the situation "doesn't look good."

"If all of a sudden you have somebody stand up and say 'hey, I need immunity,' you know, it kinda raises your eyebrows," he said.