SAN FRANCISCO, Dec. 26 (Xinhua) -- U.S. northwestern city of San Francisco filed a federal lawsuit on Tuesday against the U.S. Department of Defense over its failure to enforce an effective gun background check of service members that would have prevented killing of innocent people.

The lawsuit, filed in federal court in Virginia by San Francisco, accused the U.S. defense department of failing to honor its legal obligation to notify the Federal Bureau of Investigation (FBI) when a member of the military is convicted of a crime that would bar them from buying or possessing firearms.

Together with two other cities of New York and Philadelphia, San Francisco has also listed as defendants the U.S. Army, Navy, Air Force and a host of high-ranking Pentagon officials, including Secretary of Defense James Mattis, according to a civil action complaint filed to the district court for the Alexandria Division of the East District of Virginia.

The lawsuit came in response to a mass killing of 26 people at a church in Texas last month by Devin Kelley, a former member of the Air Force who committed the manslaughter with an assault-style rifle.

Kelley, who killed himself shortly after the Texas shooting, was convicted of assaulting his wife and young stepson in 2012. He was sentenced to 12 months' confinement in San Diego, California, and given a bad-conduct discharge.

"Had Defendants simply followed the law, that shooter never should have been able to purchase the weapon he used," said the complaint.

According to federal law, the prior conviction meted out to Kelley should have prevented him from purchasing or possessing a firearm.

The U.S. Air Force has acknowledged its failure to report the conviction to the FBI, whose database was used by local law enforcement officials to conduct background checks on gun permit applications and monitor purchases.