The CFPB was established during the Obama administration as a bulwark against predatory banking practices.
There have been questions as to whether Trump has the power to nominate Mulvaney to the post. The White House made the case today that President Trump does have the power to do this under the authority of the Federal Vacancies Reform Act, calling the interim appointment a "typical, routine move."
A senior administration official told reporters Saturday that Cordray's actions seem to indicate he's "trying to provoke" a legal battle.
Cordray, however, said he was only acting under the legal authority given him.
"The law authorized me to appoint a deputy director, and I did so," Cordray said in an interview with the Washington Post. "My understanding of the law is that the deputy director serves as the acting director upon my resignation. If there are disagreements about these issues, the appropriate place to settle them would be in the courts."
Legal experts and politicians appear to be split on the issue of the CFPB director's succession.
The White House elaborated on its defense of the nomination, referencing the support of the Justice Department Office of Legal Counsel.
Trump tweeted on the matter, calling the CFPB a "total disaster as run by the former administration's pick," and promising: "We will bring it back to life!"