Rep. James Clyburn (D-S.C.) said Tuesday that he's urged the Congressional Black Caucus (CBC) to formally back outgoing Speaker Nancy Pelosi's (D-Calif.) bid to become minority leader.

Clyburn reiterated his support for Pelosi, who's fighting to remain as Democratic leader in the minority for the next Congress, and urged fellow members of the CBC to do the same.

"I asked the members of the caucus to do that as well," Clyburn said of his plea to the CBC to back Pelosi, during an appearance on CNN. "Last night I asked them to do that. They said we may do that."

Rep. Barbara Lee (D-Calif.), the chairwoman of the Black Caucus, told The Hill on Monday evening that she was "reserving judgment" about Pelosi's leadership candidacy.

The CBC is particularly looking to study the deal Pelosi had cut over the weekend to keep Clyburn in the third-ranking position of the House Democratic leadership by creating a new position to which the outgoing whip would have to be elected. CBC members had hoped Clyburn would remain in the position of whip, the second-ranking job in the minority. Under the deal created by Pelosi, outgoing Majority Leader Steny Hoyer (D-Md.) would become the new whip.

"What we are doing is saying that everybody will maintain their relative position in the 112th," Clyburn said. "So there is nothing unusual about this, and I was very pleased with the agreement that Speaker Pelosi came with."