Several Republican lawmakers said Tuesday they are encouraging South Carolina Rep. Trey Gowdy to run for majority leader.

Gowdy, the former federal prosecutor who was elected in 2010 and leads the House Benghazi committee, is not currently running for the seat. But Utah Rep. Jason Chaffetz said on Fox News Tuesday he thinks Gowdy would run if enough people offered support to him.

“I think the Republican conference needs somebody who can unite the body, who can represent us far and wide, who can articulate the message,” Chaffetz said. “And you know what? Trey Gowdy is the best person to do that. Having spoken to him, I actually think he’ll do it if we get behind him and support it.”

Another lawmaker, Utah Rep. Mia Love, issued a statement saying she would like to see Gowdy run.

“I am more convinced than ever that it is time for Congress to trust the American people — and it will take the right leader in the right role to make that a reality,” Love said. “That is why I am asking my colleagues to join me in drafting Trey Gowdy to be our majority leader.”

A spokeswoman for Gowdy said: “Chairman Gowdy is focused on the Benghazi Committee and will serve in that capacity so long as the Committee exists. He appreciates the confidence of his colleagues and looks forward to tonight’s Conference discussion.”

Majority leader Kevin McCarthy is running to replace John Boehner as speaker. Louisiana Rep. Steve Scalise, the majority whip, and Georgia Rep. Tom Price, the chairman of the House budget committee, are both planning to run for majority leader should McCarthy become speaker.

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