Republican and Democratic senators have joined forces on legislation to strengthen the FBI database of prohibited gun buyers.
The move comes after the Air Force failed to report the criminal history of a gunman who killed 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 number two Republican, John Cornyn of Texas, would ensure that federal agencies, such as the Defence Department, and states accurately report relevant criminal information to the FBI.
The Air Force has acknowledged the Sutherland Springs gunman, Devin P Kelley, should have had his name and domestic violence conviction submitted to the National Criminal Information Centre database.
The bill would penalise federal agencies that fail to properly report required records and reward states that comply by providing them with federal grant preferences.
Mr Cornyn said agencies and state governments have for years failed to forward legally-required records without consequences.
He added: "Just one record that's not properly reported can lead to tragedy, as the country saw last week in Sutherland Springs, Texas.
"This bill aims to help fix what's become a nationwide, systemic problem, so we can better prevent criminals and domestic abusers from obtaining firearms."
Democratic Senator Chris Murphy, of Connecticut, a fierce proponent of gun restrictions, said much more needs to be done on the issue of gun violence, but he believes the bill will help ensure thousands of dangerous people are prevented from buying guns.
"It represents the strongest update to the background checks system in a decade and provides the foundation for more compromise in the future," Mr Murphy said.
The measure's prospects in the Senate are unclear despite Mr Cornyn's backing and it faces an uncertain future in the GOP-run House.
The bill would penalise agencies that fail to forward required information by prohibiting political appointees from receiving any bonus pay.
The legislation also seeks to improve accountability by publicly reporting which agencies and states fail to provide the required records.
Anyone who purchases a gun from a federally-licensed dealer must pass a background check.
People convicted in any court of domestic violence are prohibited from buying a gun but the Air Force has acknowledged it failed to tell the FBI about the assault conviction of Kelley, a former airman who killed more than two dozen in the Texas church on November 5.
That failure made it possible for Kelley to acquire weapons that federal law prohibited him from buying or possessing after his 2012 conviction.
The Army has also said it failed to alert the FBI to soldiers' criminal history in a "significant amount" of cases.