House Minority Leader Kevin McCarthy (R-CA) on Thursday appeared to back down after reports suggested that he would punish Rep. Liz Cheney (R-WY) if she participated in an investigation of the Jan. 6 attack on the U.S. Capitol.

At his weekly GOP press conference, McCarthy claimed that he was not threatening to strip Cheney's committee assignments despite reports that said otherwise. Earlier in the day, Cheney said that she was "honored" to serve on the Jan. 6 select committee after being given the assignment by House Speaker Nancy Pelosi (D-CA).

"Uh, I'm not making any threats about committee assignments," McCarthy told reporters before complaining that Cheney had accepted the select committee assignment from Pelosi, who is a Democrat.

"You get committees from your conference," the GOP leader said. "I don't know in history where someone would go and get their committee assignments from the Speaker and expect to have them from the conference as well."

CNN's Manu Raju pressed McCarthy: "She can lose her committee assignments for wanting to investigate what happened."

"Let me be very clear," McCarthy insisted. "I'm not threatening anybody with committee assignments. What I'm saying is, it was shocking to me that if a person is a Republican, they get their committee assignments from the Republican conference."

"For somebody to accept committee assignments from Speaker Pelosi, that's unprecedented," he concluded.