WASHINGTON — In 1996, after a concerted push from Senator Frank Lautenberg of New Jersey, Congress made it illegal for anyone convicted of domestic abuse — even a misdemeanor — to buy a firearm. Mr. Lautenberg, who died in 2013, liked to say the law was “dedicated to the simple principle that wife-beaters and child abusers should not have guns.”

Yet in the two decades since, a large percentage of the perpetrators of mass shootings and other violent crimes have had run-ins with the law over spousal abuse — and have had little problem acquiring deadly arsenals. On Sunday, Devin P. Kelley joined that fraternity, gunning down 26 people at a church in Texas with an AR-15 military-style rifle that he bought two years after the Air Force convicted him of beating his wife and breaking his young stepson’s skull.

The Air Force on Monday acknowledged that Mr. Kelley’s domestic violence offense, clearly one that should have made him ineligible for a firearm, had not been entered into the National Criminal Information Center database. It pledged to conduct a sweeping review of all cases to determine if they had been properly reported.

“I am deeply disturbed — in fact, outraged — that this domestic violence conviction was apparently never reported, and what concerns me equally is the possibility that it’s only one example of nonreporting by the Department of Defense,” said Senator Richard Blumenthal, Democrat of Connecticut, in an interview on Monday evening.