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.
What checks are currently in place?
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.
What does the bipartisan bill suggest?
After that shooting, a bipartisan bill was introduced by 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".
What does Trump think about gun control?
Trump's view on gun control has changed over time, but he ran as an anti-gun control candidate in the 2016 election.
Last year the president told a National Rifle Association convention that he would "never, ever infringe" on the constitutional right to keep and bear arms.
Trump has repeatedly emphasized the role of shooter's mental health for Florida's school attack, but last year he repealed an Obama-era rule that allowed people on certain mental health benefits to be entered onto the database.Trump 'supportive' of improved gun checks
So many signs that the Florida shooter was mentally disturbed, even expelled from school for bad and erratic behavior. Neighbors and classmates knew he was a big problem. Must always report such instances to authorities, again and again!
Florida suspect Nikolas Cruz, 19, had been investigated by the authorities for posting disturbing content online, according to reports.
Survivors from the Marjory Stoneman Douglas High School shooting have been vocal since last week's attack about the need for changes to existing laws around gun control.
They have organised a march on Washington on 24 March, and want simultaneous demonstrations to happen nationally.
Other students across the US have also proposed other actions such as staging national school walk-outs.
On Saturday Parkland students, their parents and some politicians took part in an emotionally-charged rally in nearby Fort Lauderdale.