(CNN) A showdown over the leadership of a major consumer fraud protection agency was underway Monday, as both President Donald Trump's pick to lead the Consumer Financial Protection Bureau and the person tapped by its former director showed up to work.

Sunday night, lawyers for Leandra English, whom Richard Cordray named the effective acting director when he resigned on Friday, filed a lawsuit in the US District Court for the District of Columbia seeking to halt the appointment of Mick Mulvaney, who serves as head of the Office of Management and Budget and is also named in the lawsuit.

Justice Department prosecutor Brett Shumate said the DOJ was expecting to file an order Monday evening responding to the lawsuit, and questioned whether English met the standard of irreparable harm required in the case.

Judge Timothy Kelly, a Trump-appointed judge who was confirmed by the Senate in September, said he would review the DOJ's filing and decide on the next steps in the case after that.

English's move marked a stunning turn of events at the agency, which was created after the financial crisis to protect consumers and keep an eye on Wall Street. While serving in Congress, Mulvaney voted in favor of killing the bureau, arguing it has too much power and issues unduly harsh regulations, and he has worked alongside Trump to roll back some of the agency's rules.

White House press secretary Sarah Sanders said Monday that the administration does not have anything against English.

"I am saying we want director Mulvaney to lead this agency, and that is a decision that the President is allowed to make and one that he has made and has legal authority to do so," Sanders said.

Both Mulvaney and English were present at the CFBP Monday morning. Mulvaney was given full access to the CFPB director's office with "full cooperation" from its staff, a senior White House official told CNN, adding that the OMB director brought doughnuts for his new staff. English, according to a source familiar with the matter, also was present at the bureau Monday morning, but it was not immediately clear if she and Mulvaney interacted. Mulvaney's communications director tweeted a photo of his boss "hard at work" in his new position.

@MickMulvaneyOMB sitting in director's office. Already hard at work as acting director at cfpb. pic.twitter.com/BKISYfduY7 — john czwartacki (@CZ) November 27, 2017

Mulvaney also addressed reporters Monday afternoon, where he announced a 30-day hiring freeze effective immediately and a 30-day "immediate freeze on any new rules, regulations and guidance."

"Anything that's in the pipeline stops for at least 30 days while I get a chance to see exactly what's going on," Mulvaney said.

In a remarkable example of the power struggle and resulting confusion, English and Mulvaney issued dueling emails to staff Monday morning. English's was brief, offering appreciation "to all of you for your service." Mulvaney's email directly disputed English's, asking staff to disregard her instructions and to inform the agency's general counsel of any communications from her related to bureau duties.

Both emails were signed "acting director."

Judge Timothy J. Kelly has been assigned to the case filed by English. Kelly, a former staffer of Sen. Chuck Grassley on the Senate Judiciary Committee, was nominated by Trump and confirmed by the Senate in September.

In their court filing, attorneys for English argue she is entitled to the position under the Dodd-Frank Wall Street reform law, which created the agency and says the deputy director becomes acting director when the agency's top spot is vacant. When Cordray resigned , he named English, then his chief of staff, as deputy director, establishing her as the bureau's acting director.

But Trump named Mulvaney the head of the agency shortly after Cordray appointed English, signaling a showdown over who will take charge of the federal watchdog agency.

"The President's attempt to install a White House official at the head of an independent agency — while allowing that officer to simultaneously serve in the White House — is unprecedented," said English's lawyer, Deepak Gupta of the law firm Gupta Wessler, in the statement on Sunday. "The law is clear: Ms. English is acting director of the Consumer Financial Protection Bureau until the Senate confirms a new director."

When asked about the controversy, Mulvaney said he plans to return to work Tuesday, but also said he would "absolutely follow the law" if the courts block him from the agency.

"If the court decides to issue a temporary restraining order, order me not to come into the building, I will absolutely follow the law," Mulvaney said. "I want to make that perfectly clear. We follow the law here; that's what we do in the executive branch. I'm not concerned about it. I'm going forward tonight and tomorrow assuming that I'll be here, and I'll be here until the court or the President tells me otherwise."

The White House defended its decision Sunday night despite English's court filing.

"The administration is aware of the suit filed this evening by Deputy Director English. However the law is clear: Director Mulvaney is the Acting Director of the CFPB," Sanders said in a statement. "Now that the CFPB's own General Counsel -- who was hired under Richard Cordray -- has notified the Bureau's leadership that she agrees with the Administration's and DOJ's reading of the law, there should be no question that Director Mulvaney is the Acting Director. It is unfortunate that Mr. Cordray decided to put his political ambition above the interests of consumers with this stunt."

On Saturday morning, the White House defended Trump's choice of Mulvaney as the consumer agency's acting director, calling it a "typical, routine move."

Mulvaney and his team were not expecting a showdown at the agency Monday morning, a source close to the OMB director told CNN. They view Mulvaney's appointment as something that the Justice Department, consumer agency lawyers and staff agree upon and expect a normal transition, the source said.

"Rumors that I'm going to set the place on fire, or blow it up or lock the doors are completely false. I'm a member of the executive branch of government -- we intend to execute the laws of the United States, including the revisions of Dodd-Frank," Mulvaney said to reporters Monday afternoon.

"Anybody who thinks that a Trump administration CFPB would be the same as an Obama administration ... CFPB is simply being naive. Elections have consequences at every agency, and that includes the CFPB," he later added.

Arkansas Sen. Tom Cotton, a member of the Banking Committee and longtime critic of the Consumer Financial Protection Bureau, called English's lawsuit "just the latest lawless action" by the agency, which he labeled "rogue" and "unconstitutional" in a statement Sunday night.

"The President should fire her immediately and anyone who disobeys Director Mulvaney's orders should also be fired summarily," Cotton said. "The Constitution and the law must prevail against the supposed resistance."

But Sen. Dick Durbin, D-Illinois, said on CNN's "State of the Union" Sunday that the White House's move was intentionally aimed at dismantling the agency.

"Wall Street hates it like the devil hates holy water. And they're trying to put an end to it with Mr. Mulvaney stepping into Cordray's spot," he said. "But the statute is specific, it's clear, and it says that the deputy shall take over."