A federal appeals court in Washington voted Monday to reinstate the heads of two independent government agencies that oversee labor disputes, extending a legal standoff touched off by President Trump’s attempt to fire them.

The boards work to protect the rights of federal employees and unionized workers, and the once-obscure bodies have been thrust into the spotlight as Mr. Trump moves quickly to cut thousands of jobs and strip federal workers of the protections that have proven obstacles to his downsizing efforts.

The decision hinged on a contested legal precedent that shields the officers of these types of boards from political pressure by preventing them from being removed without cause. It tees up an expected finale in which the Supreme Court will be asked to issue the final word on whether Mr. Trump can unilaterally shake up the boards’ leadership.

By a 7-4 vote, the court voided an earlier decision by a divided three-judge panel that had cleared the way for the Trump administration to remove Cathy Harris and Gwynne A. Wilcox — both appointed by former President Joseph R. Biden Jr. — from their posts at the Merit Systems Protection Board and the National Labor Relations Board.

Both women found themselves targets of the president amid his broader campaign to centralize power and eliminate constraints on his ability to fire federal workers and decimate the federal service.