The military branch missed two opportunities to stop Kelley from buying guns after he was accused of violence in 2012, according to officials and military documents obtained by the publication.
Kelley had been court-martialed in 2012 for assaulting his wife and stepson, including cracking the infant's skull.
Authorities also missed a third chance to put an alert on Kelley when a Pentagon review of cases did not include his.
The report comes after the Air Force revealed on Monday it had failed to enter Kelley's domestic violence conviction in a federal database used for background checks on gun sales.
Kelley killed 26 people on Sunday when he opened fire on a congregation at a Baptist church in Sutherland Springs, Texas.
The 2012 conviction likely would have blocked Kelley from purchasing the military-style rifle that he used in the shooting, as well as three other guns he had purchased over the past four years, according to The New York Times.
“The Air Force has launched a review of how the service handled the criminal records of former Airman Devin P. Kelley following his 2012 domestic violence conviction,” the Air Force said in a statement provided to The Hill on Monday.
“Federal law prohibited him from buying or possessing firearms after this conviction.”
Air Force Secretary Heather Wilson said on Thursday the service had spoken to more than 100 people on how the Texas church shooter’s criminal history had been overlooked, and said a draft report on the matter would be expected next week.