Amid a controversy over who will run the top consumer watchdog, Mick Mulvaney showed up Monday morning at the Consumer Financial Protection Bureau and took charge of the office's operations, according to a senior White House official.

President Donald Trump tapped Mulvaney, who doubles as head of the Office of Management and Budget, to run the financial industry oversight office, but there is a dispute over whether he has that authority.

However, Mulvaney was greeted by CFPB staff to start the week and he received his transition binders. He also was given access to the director's office and is said to be getting "full cooperation" from the holdover staff, according to the White House official.

@MickMulvaneyOMB sitting in director's office. Already hard at work as acting director at cfpb.

In an apparent effort to start the day off right, Mulvaney was seen carrying a bag from Dunkin' Donuts.

Richard Cordray formerly ran the office but announced nearly two weeks ago that he would be leaving before the end of November. On his way out the door, Cordray promoted his former chief of staff, Leandra English, to succeed him as acting director if the White House had not intervened.

Mulvaney sent a memo to staff on Monday instructing them to disregard "any instructions" they receive from English, according to Reuters.

Shortly after Cordray's resignation became official Friday, the White House formally announced Mulvaney as its choice to lead the agency on an interim basis until a full-time director is named. The dueling appointments set off a legal back-and-forth over the weekend resulting in disputing claims over who should take the job. The White House's Office of Legal Counsel pointed to a 2016 court decision prioritizing the executive branch's authority.

Though Trump already had indicated he wanted Mulvaney to run the office on an interim basis until a full-time director is named, Cordray named English as his successor.

Insisting that she is the rightful director, English filed a lawsuit in a District of Columbia federal court to block Mulvaney from taking over. The lawsuit sought a temporary restraining order from installing Mulvaney as the interim director.

The Trump administration believes it will prevail, in large part because the CFPB's own general counsel issued a ruling that supports the White House move. Further, English filed the lawsuit on her own behalf, without the agency's backing.

The bureau was set up after the financial crisis as part of the Dodd-Frank banking reforms. It has become a central bone of contention between Democrats who believe Wall Street needs tougher reforms and Republicans who hold the office up as an example of government overreach.

Trump and White House officials have declined opportunities to fire Cordray, citing a fear the outgoing director would use the move as fuel for his second political act, as CNBC has reported.

Critics of the CFPB say the agency's authority is ill-defined. That point has flared up again, with English insisting that Dodd-Frank gives the CFPB director the right to name his successor, while the administration maintains that the Federal Vacancies Reform Act supersedes and gives the president the authority to name agency heads.

The full English lawsuit: