The United States Air Force Academy near Colorado Springs.

Matthew Staver for The New York Times

A review by the United States Air Force has found several dozen cases in which the military failed to report service members charged with or convicted of serious crimes to the federal gun background-check database, Air Force officials said on Tuesday.

The review came after the Air Force disclosed that it had failed to report the domestic violence conviction of Devin P. Kelley, the gunman who opened fire at a church in Texas earlier this month. Under federal law, Mr. Kelley’s court-martial conviction for domestic assault should have prevented him from purchasing at a gun store the rifle he used in the attack, as well as other guns he acquired over the past four years.

After the Air Force admitted on Nov. 6 that officials at Holloman Air Force Base in New Mexico had failed to report the results of Mr. Kelley’s court-martial to the federal background database, it launched an investigation into how many other serious incidents had not been reported.

Although officials have examined only a portion of the cases across the Air Force that should have been reported, several dozen cases have already surfaced that were not reported as required. In the weeks since the review began, those cases have been corrected and reported, Air Force officials said.

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