WASHINGTON — The Supreme Court on Monday agreed to decide whether President Obama violated the Constitution last year when he bypassed the Senate in making three recess appointments to the National Labor Relations Board.

The court will review a January decision from a three-judge panel of a federal appeals court in Washington that ruled against the administration on very broad grounds, calling into question the constitutionality of many recess appointments by presidents of both parties.

The appeals court judges agreed that presidents may avoid the usual Senate confirmation process only during the recesses between formal sessions of Congress, which generally happen once a year. Two of the judges went further and said that presidents may fill only vacancies that arose during that same recess.

If the Supreme Court agrees on both points, it would markedly narrow the president’s recess appointment power.