Cordray, now confirmed, steers clear of politics

Republicans have long been critical of the bureau, created as part of the Dodd-Frank financial reform law, and blocked Cordray's nomination to lead it for years. The president installed Cordray via a recess appointment in 2012, and a recent deal on several stalled nominees finally saw his official confirmation in July.

Now officially on the job, Cordray said his team is hard at work overhauling a "broken" mortgage market.

"We have been refashioning that market to make it safer and easier for consumers to access, and that will continue to be a priority for us," he said.

He added that the bureau is working to thread the needle between cracking down on risky lending and hidden costs, while ensuring that credit remains accessible and supporting the housing market.

He also expressed frustration with continued problems in the mortgage servicing industry, as borrowers struggling for assistance continue to have difficulty obtaining support. His remarks came one day after the CFPB released a report documenting ongoing servicing problems at mortgage lenders across the industry.

Cordray came to the CFPB as a top adviser to Elizabeth Warren (D-Mass.), the longtime consumer advocate who came up with the idea for the agency and was chosen by the president to set it up. Cordray was ultimately nominated to lead the bureau once established, in part because Republicans refused to confirm Warren. She is now a freshman senator, and Cordray said they speak "periodically."

"She's a friend of mine," he said.