WASHINGTON—The Justice Department asked the Supreme Court on Monday to block a judge’s order requiring it to reinstate more than 16,000 federal employees, as administration officials vow to seek the justices’ intervention in clearing away lower-court rulings that have slowed Trump policies.

The Trump administration asked the Supreme Court on Monday to put on hold a federal judge’s ruling reinstating thousands of probationary federal employees who were fired as part of the government’s efforts to quickly downsize its workforce.