(CNN) Former Rep. Barney Frank pushed back Saturday on the White House's assertion that President Donald Trump has the authority to appoint an interim director of the Consumer Financial Protection Bureau, saying the independence of watchdog agency was a key consideration when Congress passed the law to create it in 2010.

"We gave a lot of attention to how to structure the CFPB and how to protect its independence, because its job is to go after some very powerful forces in the economy," the Massachusetts Democrat, who authored the law with then-Connecticut Democratic Sen. Chris Dodd, told CNN in an interview. He added: "The point is, we intend what [former CFPB Director Richard] Cordray was doing to have this kind of autonomy."

The Dodd-Frank Wall Street reform law designated that the watchdog's deputy director would serve as acting director in the event of a vacancy specifically to give the agency independence from the White House, Frank said. When Cordray resigned Friday, he appointed the agency's chief of staff, Leandra English, to serve as its deputy director, teeing her up to take over as the bureau's acting director.

But hours after Cordray tendered his resignation, the White House announced that Trump had chosen Office of Management and Budget Director Mick Mulvaney to serve as acting director, setting off a possible legal fight over the leadership of the agency.

"Director Mulvaney will serve as acting director until a permanent director is nominated and confirmed," the White House said in a statement Friday.

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