(CNN) Sen. Lindsey Graham said Tuesday that he will investigate how the FBI handled the investigations into Russian interference in the 2016 elections and Hillary Clinton's email controversy if he becomes chairman of the Senate Judiciary Committee.

"Totally," the South Carolina Republican told CNN when asked if he would look into the FBI's handling of those probes. "The oversight function will be very much front and center."

Graham has been a longtime critic of the FBI's handling of those investigations -- and has called for a second special counsel to investigate what happened. And if Iowa Republican Sen. Chuck Grassley steps aside from running the Senate Judiciary Committee to chair the Senate Finance Committee, as is widely expected, Graham would be poised to run the powerful panel that oversees the FBI. Graham's comments are the latest sign that the Senate GOP will be a counterbalance of sorts to House Democrats, who plan to end the House Republican probe into the FBI and launch a flurry of new investigations in their new majority next year.

Graham also said Tuesday that he would support Senate passage of a bill to protect special counsels like Robert Mueller from political pressure, even though he said, "I don't see any threat to Mueller." Democrats have demanded quick passage of that bill after President Donald Trump fired Jeff Sessions as attorney general last week and named Mueller critic Matt Whitaker to the post as acting AG.

"I'd support it if it came to the floor, but I don't see any threat to Mueller," said Graham, who cosponsored the special counsel bill that the Senate Judiciary Committee approved this year. "The idea of a check and balance going forward makes sense to me. ... I don't see an imminent threat to Mueller, but I've always been supportive of the idea."

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