A friend’s claim that the man accused of opening fire last week on two military facilities in Tennessee bought powerful guns over the Internet has renewed attention to online firearm bazaars, a lightly regulated world where buyers and sellers can set up purchases without background checks.

Over the weekend, a friend of Mohammod Youssuf Abdulazeez, the man authorities say shot and killed four U.S. Marines and one sailor, said that Mr. Abdulazeez had long been fascinated with guns and within the last year or so had purchased...