AUSTIN — Gov. Greg Abbott, in his first public comments after a Florida school shooting spurred a national debate on gun safety, said Tuesday that he supports fixing the federally maintained database for background checks on gun buyers and renewed discussion of school safety and mental illness.

"It's clear that the status quo is unacceptable and that everybody in every state must take action," Abbott said after casting a ballot in the GOP primary on the first day of early voting.

But he ducked questions on whether semiautomatic weapons should be banned and the state should let judges temporarily take guns away from people said by relatives to be on the verge of violence.

Abbott also declined to respond when a reporter asked if he agrees with Florida Gov. Rick Scott's call for FBI Director Christopher Wray to resign after Wray's acknowledgement that some bureau "protocols were not followed" after a January tip regarding Parkland, Fla., school shooter Nikolas Cruz.

Abbott, a former state attorney general, said school gun safety standards in Texas should be reviewed, to "see to what extent they must be updated."

Gov. Greg Abbott urged voters to avoid long lines by casting early votes, as he did Tuesday in Austin. (Robert T. Garrett/The Dallas Morning News)

He did not elaborate.

Abbott also called for fixing the National Instant Criminal Background Check System or NICS, which the FBI maintains.

Before both the Florida school shooting and last year's church shooting in Sutherland Springs, government agencies failed to submit information to NICS, he said.

In the case of Sutherland Springs shooter Devin Patrick Kelley, Abbott said, "There was an error by the U.S. Air Force by not entering data that could have prevented the shooter from being able to purchase a gun."

Abbott did not explicitly endorse a proposal by Texas Sen. John Cornyn to improve agencies' reporting to the database. He noted, though, that several bills have been filed in Congress. "Some of those proposals should be strongly considered and meaningfully passed," Abbott said.

"We need to get government at all levels to input data into the NICS system ... as well as be responsible for not doing so."

Abbott spoke more vaguely of a societal need to sort out the mentally ill on the verge of committing violence from others who are mentally ill.

"Not all mental health issues are going to lead to someone using a gun to harm others," he emphasized. "We need to find out a way to identify and distinguish between mental health issues that would cause a gun crime and those that would not cause a gun crime."

He added, "We need to empower local law enforcement to respond to red flags."

Abbott said he wants to participate in a national dialogue of gun safety. This weekend, he plans to travel to Washington, D.C., for a meeting of the Republican Governors Association.

"We will be meeting with the president and his team to talk about this on a national level. This is something that requires a national response, all 50 states working collaboratively together to find out the right solutions," Abbott said.

On state politics, Abbott declined to say whether he voted for Attorney General Ken Paxton, who is under indictment for alleged securities fraud; and Agriculture Commissioner Sid Miller and Land Commissioner George P. Bush, who have been criticized for alleged ethical improprieties. All three have denied any wrongdoing.

Abbott defended his active campaigning against three House GOP incumbents, including West University Place Rep. Sarah Davis. He was to campaign for her opponent Susanna Dokupil at a rally in Bellaire late Tuesday.