The Trump administration asked the Supreme Court on Wednesday to let it remove the leaders of two independent agencies while their challenges to their dismissals move forward in court.

In addition to asking the justices to pause an appeals court ruling requiring the officials’ reinstatements, the administration asked the court to grant review of the cases and schedule arguments at a special session of the court in May, with a decision to follow by July.

“We acknowledge the concerns surrounding litigating and deciding the important questions raised by these cases on such a short timeline,” wrote D. John Sauer, the solicitor general.

But he said the alternative was unacceptable, as it would allow the two agencies, the Merit Systems Protection Board and the National Labor Relations Board, to be overseen by officials hostile to the administration’s goals.

“The president should not be forced to delegate his executive power to agency heads who are demonstrably at odds with the administration’s policy objectives for a single day — much less for the months that it would likely take for the courts to resolve this litigation,” Mr. Sauer wrote.

If the Supreme Court does not act, he wrote, “the president might be forced to continue entrusting executive power to fired officers for more than a quarter of his four-year term.”

The emergency application was the latest in a series of requests asking the Supreme Court to step in after federal judges blocked the administration’s initiatives on personnel, spending, immigration and citizenship. The court’s rulings on such requests to date have been tentative and technical.

The administration’s emergency application seeks a more categorical ruling, taking aim at a foundational 90-year-old legal precedent that said Congress can limit the president’s power to fire the heads of agencies and so shield them from politics.

Some conservative justices have said they would overrule the precedent, arguing that it unconstitutionally infringed the power of the president to lead the executive branch. That could significantly expand President Trump’s ability to fire the leaders of agencies without cause despite laws requiring a good reason for the terminations.

The U.S. Court of Appeals for the District of Columbia Circuit cited the precedent on Monday, ruling by a 7-to-4 vote that the administration must reinstate Cathy Harris to the Merit Systems Protection Board and Gwynne A. Wilcox to the National Labor Relations Board. Both women had been appointed by President Joseph R. Biden Jr.

Weakening the power of the two boards is part of President Trump’s campaign to reshape the government and the workplace. The Merit Systems Protection Board reviews federal employment disputes, while the National Labor Relations Board safeguards the rights of private sector workers.

Mr. Trump fired the two officials in February. Though federal laws required him to cite a cause, he gave no reasons.

In Monday’s appeals court ruling, which was unsigned, the majority wrote that a 1935 Supreme Court precedent, Humphrey’s Executor v. United States, barred the firings.

That case concerned a federal law that protected commissioners of the Federal Trade Commission, saying they could be removed only for “inefficiency, neglect of duty or malfeasance in office.”

President Franklin D. Roosevelt nonetheless fired a commissioner, William Humphrey. The only reason he gave was that Mr. Humphrey’s actions were not aligned with the administration’s policy goals.

Mr. Humphrey died a few months later, and his estate sued to recover the pay he would have received in that time. The Supreme Court unanimously ruled that the firing had been unlawful and that the statute at issue was constitutional.

In 2020, the Supreme Court seemed to lay the groundwork for overruling that precedent in a case involving the Consumer Financial Protection Bureau.

“In our constitutional system,” Chief Justice John G. Roberts Jr. wrote, “the executive power belongs to the president, and that power generally includes the ability to supervise and remove the agents who wield executive power in his stead.”

But the chief justice drew distinctions between agencies led by a single director, like the consumer bureau, and bodies with multiple members, like the two boards. Several justices said they did not think the differences were meaningful.

The general reasoning in the chief justice’s opinion left Humphrey’s Executor on life support. Two members of the court — Justices Clarence Thomas and Neil M. Gorsuch — would have pulled the plug right away.

“The decision in Humphrey’s Executor poses a direct threat to our constitutional structure and, as a result, the liberty of the American people,” Justice Thomas wrote.

He added: “With today’s decision, the court has repudiated almost every aspect of Humphrey’s Executor. In a future case, I would repudiate what is left of this erroneous precedent.”

The appeals court’s majority said on Monday that it was required to follow the 1935 precedent. If it is to be overruled, the majority said, the Supreme Court must do so.