A federal judge said on Monday that the Trump administration’s deferred resignation program would remain paused until he ruled on its legality, hours before a deadline for roughly two million federal workers to accept incentives to quit.

Federal officials had set a deadline of 11:59 p.m. Eastern time on Monday for employees to join the resignation program, known as “Fork in the Road,” part of an Elon Musk-led initiative to drastically slash the size of the federal government. Federal workers who take the offer would receive pay through September, according to the Trump administration.

George A. O’Toole Jr., a U.S. District Court judge in the District of Massachusetts, last week stopped the Office of Personnel Management, the federal government’s human resources agency, from moving ahead with the program until Monday’s hearing, forcing the government to adjust its deadline for employees to accept the offer.

It was not immediately clear when Judge O’Toole would rule.

“The program is NOT being blocked or canceled,” the agency wrote in a social media post last week. “The government will honor the deferred resignation offer.”

The Trump administration has said that more than 65,000 federal workers accepted the deferred resignation offer, representing less than 3 percent of all 2.3 million federal workers, excluding the military and the Postal Service. Mr. Musk, who is spearheading the Trump administration’s efforts to whittle down the federal government, had circulated an estimate that the offer could lure 5 to 10 percent of the federal work force to leave.

Roughly 150,000 federal workers, or 7 percent, voluntarily leave the government every year.

The liberal nonprofit Democracy Forward and government unions representing hundreds of thousands of federal workers — the American Federation of Government Employees; the American Federation of State, County and Municipal Employees; and the National Association of Government Employees — had sued to stop the resignation program. They argued that it was unlawful in part because Congress had not yet appropriated funds to compensate workers the Trump administration was promising to pay.