In its brief filed late Thursday asking the Supreme Court to consider the case, the Trump administration said the question for the justices was momentous.

“The stakes are indisputably high: The court of appeals concluded that the president acted in bad faith with religious animus when, after consulting with three members of his cabinet, he placed a brief pause on entry from six countries that present heightened risks of terrorism,” the brief said.

It added that the appeals court had gone badly astray.

“The court did not dispute that the president acted at the height of his powers in instituting” the executive order’s “temporary pause on entry by nationals from certain countries that sponsor or shelter terrorism,” the brief said. The brief also said the order’s “text and operation are religion-neutral.”

The Supreme Court is back at full strength with the appointment of Justice Neil M. Gorsuch to fill a seat left vacant for more than a year after the death of Justice Antonin Scalia. The new case will be an early indication of how Justice Gorsuch affects the balance of power on the court.