Newly installed Consumer Financial Protection Bureau director Richard Cordray laid out his agenda Thursday, vowing to press ahead despite political objections and legal questions about his status as a recess appointee.

“It’s a valid appointment. I’m now the director of the bureau. . . . We now have our full authority to move forward,” Cordray said in his first public speech as the agency’s director, a day after President Obama used a recess appointment to bypass Republicans who had blocked Cordray’s confirmation in the Senate.

“The most important thing is to keep our nose to the grindstone and keep doing our work,” Cordray said in remarks at the Brookings Institution. “We will prove our own case, both to people who represent the public and to the public at large.”

As for the legal questions about his appointment — which Obama put through in less than 10 days of congressional recess, breaking with precedent — Cordray said he would “leave the details to others.”

Objections to Cordray’s recess appointment have come not only from congressional Republicans, but also outside groups such as the U.S. Chamber of Commerce, which on Thursday said Obama’s move “puts the authority of the director and the validity of the bureau’s work in legal jeopardy.”

In his speech Thursday, Cordray cast the bureau as a staunch consumer advocate that would listen to the grievances of ordinary Americans who felt they’d been misled or defrauded by financial firms. “Consumers deserve to have someone to stand on their side. They don’t expect any special favors, they just want a fair shake,” he said.

Though it didn’t have an official director until Wednesday, the bureau has been up and running since July as part of the Dodd-Frank financial regulatory overhaul, with Cordray serving as the head of its enforcement division.

The bureau’s major priorities, Cordray said, will be demanding greater transparency about consumer financial products and pursuing enforcement actions against financial firms that have defrauded consumers or otherwise violated federal rules.

Cordray said the bureau had already taken over and initiated its own investigations into such firms. But he declined to elaborate upon which cases they were focusing on or how the agency would carry out its enforcement duties — whether, for example, it would focus on lawsuits against financial firms, as Cordray had aggressively pursued in his previous job as Ohio’s state attorney general.

He did say the bureau has begun its oversight of “payday lenders, mortgage servicers, mortgage originators, private student lenders” and other “nonbank” financial firms that were largely unregulated before the passage of the Wall Street regulatory overhaul.

Cordray emphasized that the ongoing controversy about his appointment would not alter his agenda. But he also suggested that Republicans had opposed his nomination — and the recess appointment — out of principle, not partisan politics. “I’m not someone who impugns people’s motives,” he said, referring to the GOP objections. “I believe people are trying to do what’s right.”