The Supreme Court on Tuesday gave Jack Smith, the special counsel prosecuting former President Donald J. Trump, a week to respond to Mr. Trump’s emergency application asking the justices to halt an appeals court’s ruling that rejected his claim that he is absolutely immune from criminal charges.

In asking Mr. Smith to respond by Feb. 20 at 4 p.m., the justices did not set a particularly speedy schedule. The court often asks for quicker responses to emergency applications on what critics call its shadow docket. But nothing prevents Mr. Smith from filing sooner, and he probably will.

The proceedings against Mr. Trump in the trial court will remain frozen in the meantime. Unless the justices move quickly, the trial could be pushed into the heart of the 2024 campaign, or even past the election.

In asking the Supreme Court to intervene on Monday, Mr. Trump’s lawyers urged the justices to move at a deliberate pace.

“President Trump’s claim that presidents have absolute immunity from criminal prosecution for their official acts presents a novel, complex and momentous question that warrants careful consideration on appeal,” Mr. Trump’s application said.

His lawyers added that the court should take account of the election campaign and what they said were Mr. Smith’s political motives in trying to move briskly.

“Conducting a monthslong criminal trial of President Trump at the height of election season,” the filing said, “will radically disrupt President Trump’s ability to campaign against President Biden — which appears to be the whole point of the special counsel’s persistent demands for expedition.”

A three-judge panel of the U.S. Court of Appeals for the District of Columbia Circuit unanimously rejected Mr. Trump’s argument that he may not be prosecuted for actions he took while in office.

The trial had been set to start on March 4, but Judge Tanya S. Chutkan has removed it from her calendar. If the justices deny Mr. Trump’s request for a stay, it will be rescheduled.