Republican Congress have always opposed the very popular Consumer Financial Protection Bureau (CFPB)

President Trump on Friday named his budget director as the acting director of the Consumer Financial Protection Bureau, moving to take control of the agency hours after its departing leader had taken steps to install his own choice for acting chief.

By the end of the night, an agency born of the financial meltdown — and one Republicans have tried to kill from the start — had dueling directors, and there was little sense of who actually would be in charge Monday morning.

The bureaucratic standoff began Friday afternoon when Richard Cordray, the Obama-appointed leader of the bureau, abruptly announced he would leave the job at the close of business, a week earlier than anticipated. He followed up with a letter naming his chief of staff, Leandra English, as the agency’s deputy director.

The announcement came with a twist. Under the law, he said, that appointment would make the new deputy director the agency’s acting director. The move was seen as an effort to delay Mr. Trump from appointing his own director, whose confirmation could take months.

The White House retaliated, saying that the budget director, Mick Mulvaney, who once characterized the consumer protection bureau as a “sad, sick joke,” would be running the agency. He would also keep his current job as head of the Office of Management and Budget.

Mr. Mulvaney said he would assume the additional role until a permanent successor was found.

“I believe Americans deserve a C.F.P.B. that seeks to protect them while ensuring free and fair markets for all consumers,” he said in a statement. “Financial services are the engine of American democratic capitalism, and we need to let it work.”

In a letter to the consumer protection agency’s staff, Mr. Cordray named Ms. English as deputy director. Under the 2010 Dodd-Frank Act, which established the regulatory agency, the deputy director is to serve as acting director in the absence of a permanent leader, Mr. Cordray said.

The conflicting appointments were a fitting development for an agency under constant attack from Republican leaders, and it leaves supporters wondering about the agency’s future with Mr. Trump in the White House and Republicans in control of both houses of Congress.

The bureau was proposed in 2007 by Elizabeth Warren, then a Harvard law professor, but she was passed over to lead the agency after Obama administration officials became concerned that she would not be able to overcome resistance from Republicans during the confirmation process.

Instead, President Barack Obama chose Mr. Cordray, a former attorney general of Ohio whom Ms. Warren had picked to be the agency’s enforcement director. But for two years, Republicans prevented the confirmation of a director to lead the agency. The agency’s creation was also largely opposed by the banking industry, which sought to prevent Mr. Cordray’s confirmation.

In July 2013, the Senate finally agreed to allow the confirmation of Mr. Cordray, cementing a new era of expansive federal oversight of companies that lend money to consumers.

The fight over the establishment of the protection bureau made Ms. Warren a political celebrity and helped her win a bid for Congress. Later, as a senator from Massachusetts, Ms. Warren has continued to champion the bureau, which has emerged as an aggressive consumer watchdog with broad power to combat financial abuses.

On Friday, Ms. Warren defended Mr. Cordray’s decision on Facebook: “President Trump can’t override that. He can nominate the next CFPB Director — but until that nominee is confirmed by the Senate, Leandra English is the Acting Director under the Dodd-Frank Act.”

Consumer groups quickly praised Mr. Cordray, whose move appeared to be a final attempt to keep the bureau in hands that would preserve the legacy he helped create as its first director.

“Fortunately, the statute creating the C.F.P.B. says that the agency’s deputy director serves as acting director until a new director has been nominated by the president and confirmed by the Senate,” Lisa Donner, executive director of Americans for Financial Reform, said in a statement. “Mulvaney has said he is opposed to the very existence of the C.F.P.B., and as a member of Congress he voted in favor of Wall Street banks and predatory lenders — his largest donors — again and again.”

The appointment of Mr. Mulvaney, who as a Republican congressman from South Carolina was a co-sponsor of legislation to shut down the consumer bureau, had been widely anticipated. The White House said in a statement on Friday that President Trump looked forward to seeing Mr. Mulvaney take a “common sense approach” to leading the bureau’s staff.

The bureau, with its reputation as an active watchdog for the financial rights of consumers, has been a major obstacle to the Trump administration’s efforts to dismantle regulations.

Mr. Trump would have been free to make major changes at the agency as he has done at other financial regulators — many of which are run by former executives — but Mr. Cordray’s surprise move may complicate those plans. And what happens next is not entirely clear.

Instead, the agency’s next director may potentially face at least some of the resistance Mr. Cordray experienced from Republicans after he was named director.

Mr. Mulvaney’s appointment was met with opposition by consumer groups.

“Naming Mick Mulvaney — someone who’s adamantly anti-consumer — rewards financial predators and fails to put consumers first,” Michael Calhoun, the president of the Center for Responsible Lending, said in a statement.

Ms. English is no stranger to the consumer protection bureau. She helped start the agency in 2011, working in several roles before leaving to join the Office of Management and Budget, according to the bureau’s website. She returned in January 2015 as deputy chief operating officer, left to work at the Office of Personnel Management and returned again in January 2017 as the bureau’s chief of staff.

Ms. English has a bachelor’s degree from New York University and a master’s degree from the London School of Economics.

One of the names that had been floated for the bureau’s top post was Todd J. Zywicki, a conservative law professor at George Mason University.

But consumer advocates have not been enthusiastic about any of the candidates mentioned. “Most have harshly criticized the idea of the bureau or even called for its repeal,” Ed Mierzwinski, a consumer program director at the advocacy group U.S. PIRG, said in a statement. “Some have questioned the idea of consumer protection itself.”

Democrats want to overly regulate every aspect of our lives.