Federal regulators dealt a blow to opponents of Holtec International Corp.’s proposal to store commercial nuclear waste in southeastern New Mexico by rejecting a hearing on their safety and environmental concerns.

The Nuclear Regulatory Commission’s Atomic Safety and Licensing Board on May 7 denied an evidentiary hearing that would have let environmental groups, including the Sierra Club and Beyond Nuclear, contest Holtec’s license application. The company wants to consolidate radioactive waste from power plants around the U.S. in...