US President Donald Trump is "supportive" of efforts to improve background checks on gun ownership, the White House says.
He spoke with Republican Senator John Cornyn about a bipartisan bill that seeks to improve the checks in place before someone can buy a gun.
It comes after authorities said the suspect in last week's Florida school shooting bought his gun legally.
Students from the school have demanded action on gun control.
"While discussions are ongoing and revisions are being considered, the president is supportive of efforts to improve the federal background check system," White House press secretary Sarah Sanders said on Monday.
Currently, federal licensed dealers must run checks on anyone trying to purchase a gun. A potential buyer presents identification and fills in a form with personal information and criminal history.
That information is then submitted to the FBI'S National Instant Criminal Background Check System (NICS), which processed more than 25 million applications last year.
But the system has holes because it relies on state and federal officials to report any criminal convictions and mental health issues that should legally stop someone buying a gun to NICS.
Its failings were put in the spotlight last year after the US Air Force admitted it had failed to flag a gunman's domestic violence conviction before he shot dead 26 people at a church in Sutherland Springs, Texas.
After that shooting, a bipartisan bill was introduced by Mr Cornyn and Democratic Senator and gun-control advocate Chris Murphy.
It requires federal agencies to better report background information thoroughly and accurately, and also proposed offering states financial incentives to do the same through a penalty and reward system.
At the time Cornyn presented it as a fix to a "nationwide, systematic problem".