The Supreme Court’s rules say that it will review a federal trial court’s ruling before an appeals court has spoken “only upon a showing that the case is of such imperative public importance as to justify deviation from normal appellate practice and to require immediate determination in this court.”

In a brief filed Friday, Mr. Francisco said, “This case satisfies that standard.”

“It involves,” he wrote, “an issue of imperative public importance: the authority of the U.S. military to determine who may serve in the nation’s armed forces.”

Trial judges have ruled that there is no evidence that service by transgender people threatens military cohesion or readiness.

“There is absolutely no support for the claim that the ongoing service of transgender people would have any negative effective on the military at all,” Judge Colleen Kollar-Kotelly, of the Federal District Court in Washington, wrote last year. “In fact, there is considerable evidence that it is the discharge and banning of such individuals that would have such effects.”

The United States Court of Appeals for the District of Columbia Circuit is set to hear an appeal of her ruling next month. The United States Court of Appeals for the Ninth Circuit, in San Francisco, has heard arguments in a separate appeal but has yet to issue a ruling. The Ninth Circuit has been the subject of scathing attacks from President Trump in recent days.