The Supreme Court on Tuesday agreed to fast-track review of the Trump administration’s sweeping tariffs, accepting a case that will test the limits of executive power and the president’s signature economic initiative.

The court set a brisk briefing schedule and said it would hear arguments in early November.

A federal appeals court last month invalidated many of President Trump’s punishing global tariffs, saying the law he relied on did not authorize the administration’s program. The import taxes remain in effect while the litigation continues.

In a 7-to-4 ruling in late August, the U.S. Court of Appeals for the Federal Circuit said the president had unlawfully used the International Emergency Economic Powers Act to impose steep taxes on major U.S. trading partners.

Last week, Mr. Trump’s lawyers urged the justices to review the ruling quickly by adding the case to the court’s calendar for the new term that begins in October. They issued a stark warning against allowing the appeals court ruling to stand, saying it threatens to unwind trade deals.

“That decision casts a pall of uncertainty upon ongoing foreign negotiations that the president has been pursuing through tariffs over the past five months, jeopardizing both already negotiated framework deals and ongoing negotiations,” according to the filing from Solicitor General D. John Sauer.

“Few cases have so clearly called out for this court’s swift resolution.”

While the Supreme Court’s conservative majority has repeatedly granted Mr. Trump’s emergency requests and cleared the way for the administration to at least temporarily put into place its policies, the tariffs case will be the first occasion for the justices to hear arguments and weigh the underlying legal merits of a key administration priority.