WASHINGTON — The Supreme Court said on Wednesday evening that it would hold a special hearing next month to assess the legality of two Biden administration initiatives aimed at addressing the coronavirus. One requires large companies to have their workers get coronavirus vaccines or be tested weekly, while the other requires health care workers at hospitals that receive federal money to be vaccinated against the virus.

The court said it would move with exceptional speed, setting the cases for argument on Friday, Jan. 7. The justices had not been scheduled to return to the bench until the following Monday.

Both sets of cases had been on what critics call the court’s shadow docket, in which the court decides emergency applications, sometimes on matters of great consequence, without full briefing and argument. The court’s decision to hear arguments on the applications may have been a response to mounting criticism of that practice.

The case concerning the requirement for large employers followed a ruling last week reinstating it from the U.S. Court of Appeals for the Sixth Circuit, in Cincinnati.

“The record establishes that Covid-19 has continued to spread, mutate, kill and block the safe return of American workers to their jobs,” Judge Jane B. Stranch wrote for a divided three-judge panel. “To protect workers, OSHA can and must be able to respond to dangers as they evolve.”

Almost immediately, more than a dozen challengers asked the Supreme Court to block the rule, issued by the Labor Department’s Occupational Safety and Health Administration, or OSHA.