The manufacturer’s air bag inflators are blamed for 11 deaths in the US alone, and more than 180 injuries worldwide.
NHTSA said it is satisfied the company has taken steps to prevent similar failures.
Covers vehicles from model years 2006 to 2014.
Group also faults the company for letting products move through the design process with unresolved problems.
The automaker is guilty of selling cars that failed US federal crash tests.
Automaker joins Honda, Toyota and Nissan in deciding against putting the troubled inflators in their cars.
Includes Corolla, Tundra, Sequoia.
Orbital ATK makes rocket propulsion systems, small arms ammunition, warhead fuses and missile controls.
Unexpected decision follows massive recalls by the Japanese automaker of vehicles equipped with air bags made by Takata Corp.
Carlos Solis is among six people killed and 64 injured by defective inflator mechanisms in Takata Corp. airbags.
Complaints include incidents related to air bags made by Japanese auto supplier Takata Corp.
More than eight million vehicles affected, according to data from Transport Canada.