House Financial Services Committee Chairman Jeb Hensarling told Consumer Financial Protection Bureau director Richard Cordray on Friday to commit to serving out his term or quit.

Referring to speculation that Cordray intends to run as a Democrat for Ohio's governor, Hensarling said that if Cordray wants to run the CFPB, "he should first commit to serving his full term. If he will not do so, the honorable course of action would be to resign and leave such decisions to his successor."

Cordray was appointed by former President Barack Obama and could serve until July 2018.

Hensarling, a critic of the bureau and of Cordray's rulemakings, has called on President Trump to fire him. Trump so far hasn't obliged.

This week, the bureau further provoked Republicans by finalizing a highly significant rule expanding access to class-action lawsuits against banks. It also undertook new mortgage regulation initiatives and selected new members to its consumer advisory board.

Last week, Hensarling threatened that Cordray might face contempt proceedings if he finalized the rule relating to class-action lawsuits.

His office didn't respond to an inquiry about whether he would follow up on that threat.

Republicans have advanced different pieces of legislation to reform the consumer bureau and strip it of some of its powers.