(CNN) -- Following the shooting in Parkland, Florida, the White House said President Donald Trump "is supportive of efforts to improve the federal background check system" for gun purchases.
Principal deputy press secretary Raj Shah said that Trump spoke with Sen. John Cornyn, a Texas Republican, on Friday about a bill he introduced with Sen. Chris Murphy, a Connecticut Democrat, that aims to strengthen how state and federal governments report offenses that could prohibit people from buying a gun.
While the House passed a bill that included this provision in December, a Senate bill with the same proposals has stalled. It's been referred to the Judiciary Committee, but it has not been taken up for a vote.
The bill came as a result of the shooting in Texas where the gunman killed 26 people at a church. The shooter had previously been imprisoned for domestic abuse, but the Air Force didn't convey that information to the National Instant Criminal Background Check System, which should have prevented him from buying the guns used in the mass shooting.
What would the bill accomplish if implemented?
It would ensure that federal and state authorities comply with existing law and require them to report criminal history records to the NICS.
The bill would hold federal agencies accountable if they fail to upload records to the background check system by blocking bonus pay for political appointees in agencies that fail to upload records to the background check system.
Under the Constitution, the federal government can't force the states to do something, so the bill uses financial incentives to encourage them to upload the records -- but it is able to mandate that federal agencies comply.
The bill wouldn't strengthen background checks, but it could have prevented Devin Kelley, the gunman in the Texas shooting, from being able to purchase a gun because he had been court-martialed for assaulting his wife and for assault on their child while serving in the Air Force and then received a "bad conduct" discharge in 2014.
The Air Force acknowledged the convictions were not properly transferred to the law enforcement database that would have allowed them to show up on an background check.
Murphy tweeted about the bill on Monday, saying the legislation alone is not an "adequate response."
"Interesting morning. Two quick thoughts: 1/ Trump's support for the FixNICS Act, my bill with @JohnCornyn, is another sign the politics of gun violence are shifting rapidly. 2/ No one should pretend this bill alone is an adequate response to this epidemic."
House lawmakers approved legislation in December to loosen gun regulations and allow those with permits for carrying concealed weapons to legally travel with those firearms to other states, which was a top priority of the National Rifle Association.
The bill was merged with two measures that have bipartisan support, including the measure to fill in holes in the NICS.
The other measure that was included would direct the Bureau of Justice Statistics to study all crimes involving firearms and report to Congress in six months about how many involved weapons with "bump fire stocks," accessories that can allow semiautomatic weapons to fire at a rate similar to automatic ones.
The shooter responsible for killing 58 people and injuring nearly 500 more attending a Las Vegas concert in October used bump stocks to direct large amounts of ammunition to the crowd, and members from both parties have called for a ban on them.
Cornyn said in December that merging the gun bills complicated the path forward in the Senate and suggested splitting off the background check fix.
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