FOUKE, Ark.—Federal and state authorities, prompted by allegations of child pornography being produced on site, executed search warrants Saturday evening at Tony Alamo Christian Ministries.

Shortly before 6 p.m., agents from the FBI, Arkansas State Police and the Arkansas Department of Human Services converged on the multiresidential compound, which sits on the equivalent of a half-mile square. For about an hour, search teams were seen entering the church and several neighboring buildings belonging to the Alamo Ministries.

Allegations that children living at the Alamo f...