Updated, 10 a.m. on Friday, March 9, with Cornyn statement he has support to pass NICS bill.

Texas Sen. John Cornyn tweeted that he has enough support to pass his bill to fix the federal background check system that allowed the Sutherland Springs church shooter to purchase a gun despite his criminal record.

Fixing the broken background check system for gun purchases will save lives. So far, 62 Senators - 31 Rs and 31 Ds - have cosponsored #FixNICS, including the Majority and Minority leaders. The House has passed it; POTUS supports it and will sign it. #nomoreSutherlandSprings — Senator John Cornyn (@JohnCornyn) March 9, 2018

"Fixing the broken background check system for gun purchases will save lives," Cornyn tweeted Thursday night. "So far, 62 Senators - 31 Rs and 31 Ds - have cosponsored

#FixNICS

, including the Majority and Minority leaders. The House has passed it; POTUS supports it and will sign it.

#nomoreSutherlandSprings

."

It's not clear when the bill will come up for a vote in the Senate. Senate Majority Leader Mitch McConnell told reporters last week that no gun-related legislation would come up the following week.

"We'd love to do that at some point," McConnell said in a brief hallway interview with reporters. "I'm hoping that there's a way forward."

Original post:

WASHINGTON — President Donald Trump is open to bipartisan efforts to improve the federal background check system for gun purchases, according to White House press secretary Sarah Huckabee Sanders.

In a statement, Sanders confirmed that Trump spoke to Texas Sen. John Cornyn on Friday about the bipartisan "Fix NICS Act," two days after 17 people were killed at Marjory Stoneman Douglas High School in Parkland, Fla.

Cornyn introduced the background check bill with Connecticut Sen. Chris Murphy following the Sutherland Springs church shooting in November. Lawmakers say the bill will penalize federal agencies that fail to report records and incentivize states to send criminal history records to the National Instant Criminal Background Check System.

"While discussions are ongoing and revisions are being considered, the President is supportive of efforts to improve the federal background check system," Sanders said in a statement.

Cornyn, the No. 2 Republican, and Murphy, one of the most vocal Democrats on gun control, filed the measure after it was revealed that the Air Force didn't send Sutherland Springs shooter Devin Kelley's court-martial and conviction for domestic violence to the FBI database used to approve gun buyers.

Kelley, who killed 26 people in a Baptist church in Sutherland Springs on Nov. 5, would not have been allowed to purchase a gun from a store if his records had been in the database.

Our churches and schools should be refuges where children and parents feel secure. Many of these shootings can be prevented. There's no reason not to advance #FixNICS to help https://t.co/0JpZDiLPOr — Senator John Cornyn (@JohnCornyn) February 15, 2018

The bill is backed by the National Rifle Association and the National Shooting Sports Foundation, and it passed through the House in December. But to the dismay of gun control advocates, the House measure was attached to a bill that would allow gun owners to use a concealed carry permit from their home state anywhere in the country.

The Senate has yet to take up the background check bill, but in December, Cornyn warned that pairing those two measures could hamper efforts to improve the background check system.

"I support both of those bills but I recognize that if you combine them, that that makes it much harder to pass the consensus bill, which is the Fix NICS bill," he said. "But I respect the House's right to do what they want to do and what they need to do there for the votes."

Gun measures stalled

After the Las Vegas shooting, it appeared Congress would pass a measure to ban bump stocks, the aftermarket accessory that allows semi-automatic weapons to fire at speeds similar to an automatic weapon. Bump stocks were found on the Las Vegas shooter's guns.

But that was more than four months ago. Instead, GOP lawmakers pushed a possible ban to the Bureau of Alcohol, Tobacco, Firearms and Explosives, which determined in 2010 that bump stocks could not be regulated by the agency.

ATF is re-examining whether bump stocks fall in the definition of a "machine gun." Meanwhile, Texas-based Slide Fire has resumed sales of the devices, and cities and states are implementing their own bans.

Last week, Republican Sen. Chuck Grassley of Iowa said he plans to sit down with Sen. Dianne Feinstein, a California Democrat, and Cornyn to discuss legislation in response to the mass shootings, according to CBS News.

And the White House announced that Trump will take part in a "listening session" this week with high school students and teachers following the deadly shooting in Florida.