A Texas group that searches for missing people is fighting a Federal Aviation Administration order to stop using drones for its searches, adding a new challenge to the agency's authority to prohibit drones in the U.S.

The group, Texas EquuSearch, has been using small drones, or unmanned aircraft, since 2006 to map search areas and conduct searches itself. In February, the FAA in an email ordered the group to stop immediately.

Texas...