A delegation of unions are calling foul on federal mine safety regulators who revoked a rule that required metal and hardrock mines to conduct safety inspections before miners go into the mines.

The United Steelworkers, AFL-CIO, and the United Mine Workers of America filed a petition for review May 2 in the U.S. Court of Appeals for the District of Columbia Circuit, contesting the rule that was finalized April 9.

The unions said the new rule...