In a court filing delivered late Monday, lawyers for Mr. Trump and Mr. Mulvaney had said that the confusion surrounding the bureau’s leadership stems from Ms. English’s “meritless claims” because the president, the Justice Department’s Office of Legal Counsel and the agency’s general counsel all agreed that Mr. Mulvaney was the acting director.

After Judge Kelly’s ruling, the White House applauded the decision.

“It’s time for the Democrats to stop enabling this brazen political stunt by a rogue employee,” Raj Shah, a White House spokesman, said in a statement, “and allow Acting Director Mulvaney to continue the bureau’s smooth transition into an agency that truly serves to help consumers.”

Judge Kelly, who was nominated by Mr. Trump and confirmed in September, said that he had not been convinced by the argument that the language in the Dodd-Frank Act superseded that in the Federal Vacancies Reform Act.

“On its face,” he said, “V.R.A. does appear to apply in this situation.”

The judge was also not swayed by the argument that Ms. English was at risk for irreparable harm, in this case losing her job as deputy director. But lawyers observing the case said that the decision on Tuesday still could keep day-to-day operations — and Ms. English’s job — at the bureau in limbo.

“This decision still leaves a lot of unanswered questions since Mulvaney will reportedly only spend three days of the week at the C.F.P.B.,” Dalié Jiménez, an associate professor of law at the University of Connecticut School of Law who spent roughly a year as a member of the founding staff at the bureau, said in an interview. “Does that mean that Leandra English as deputy director would be ‘in charge’ for the two days he’s not around? Mulvaney might move to demote or fire her at this point.”

The ruling also raises questions about the long-term path for the bureau. In a brief filed with the court, more than two dozen members of Congress — as well as former Representative Barney Frank, Democrat of Massachusetts — argued that the law clearly established Ms. English as the bureau’s acting director under Dodd-Frank, which was written to protect the agency from political influence.