Lawmakers released documents showing that senior federal officials were closely involved in a troubled gun-enforcement operation that came to light after the death of a U.S. border agent in a shootout in December.

The disclosures came at an emotional House hearing at which family members of the agent testified. Republican lawmakers are pressing to determine how high up knowledge and approval of the program went in the Bureau of Alcohol, Tobacco, Firearms and Explosives and its parent agency, the Justice Department.

Two...