WASHINGTON — Republican and Democratic senators have joined forces on legislation to strengthen the FBI database of prohibited gun buyers after the Air Force failed to report the criminal history of the gunman who slaughtered more than two dozen people at a Texas church.

Congress has taken no steps on guns in the weeks after deadly shootings in Las Vegas and Sutherland Springs, Texas. The bill, which has the backing of the Senate’s No. 2 Republican, John Cornyn of Texas, would ensure that federal agencies, such as the Defense Department, and states accurately report relevant criminal information to the FBI.

The Air Force has acknowledged that the Texas shooter, Devin P. Kelley, should have had his name and domestic violence conviction submitted to the National Criminal Information Center database.