Updated at 6:15 p.m. to include policy suggestions made during Day 1 of the gun violence summit.

AUSTIN — Texas Gov. Greg Abbott kicked off a three-day summit on gun violence Tuesday afternoon, four days after 10 Santa Fe students and teachers were killed in the country's latest mass shooting.

Abbott reminded the politicians, law enforcement and education leaders who gathered in the state Capitol about their shared mission — "to protect innocent lives in the state of Texas."

"Whether you are a Republican or a Democrat, whether you are pro-gun or believe in more gun regulations, the reality is we both want guns out of the hands of those who would try to murder our children," Abbott said. "The question is what are we, the leaders of Texas, going to do to prevent this from happening again?"

After more than two hours meeting behind closed doors, Abbott invited the media to hear the many ideas discussed on Day 1 of the summit. Some of the suggestions could be implemented before the next school year, he said, like expanding a West Texas program that identifies students who exhibit signs they may harm themselves or others and then provides them with psychiatric services over a telemedicine link.

Day 2 of the summit will address gun regulations and mental health, and on Day 3, panelists will hear from victims and families affected by gun violence.

Reading from a white legal pad, Abbott ran through a laundry list of policies suggested on Day 1, including:

"Greater parent accountability" for the actions of their children.

Rewarding students who share information about potential problems in their schools and providing "comprehensive training" on to whom they can reach out.

Developing an app for students, parents and law enforcement to give them 24/7 access to school security cameras.

Providing better training for teachers and educators who want to be armed school marshals and expanding the program so it's available to "every school at every level."

Requiring earlier intervention with students who have demonstrated mental health and behavioral challenges, and improving behavioral counseling in school districts with a focus on an increased staff-to-student ratio.

Putting together "assessment teams" to identify youth dealing with mental health challenges.

Upgrading school facilities, including entry and exit points and "hardening our schools" to make them more secure.

Requiring collaboration between law enforcement and schools and increasing law enforcement presence in schools.

Requiring schools to share threat information across levels (elementary to middle to high school).

None of the suggestions are official recommendations, the governor's staff stressed. They represent the totality of the issues discussed during Tuesday's roundtable.

1 / 5Gov. Greg Abbott hosted a roundtable discussion Tuesday about safety in Texas schools after the recent shooting at Sante Fe High School.(Ana Ramirez / Austin American-Statesman) 2 / 5Gov. Greg Abbott hosts a roundtable about safety in Texas schools at the Texas Capitol on May 22, 2018, in Austin.(Ana Ramirez / Austin American-Statesman) 3 / 5Commissioner of the Texas Education Agency, Mike Morath, gives input during a roundtable about safety in Texas schools.(Ana Ramirez / Austin American-Statesman) 4 / 5Lt. Gov. Dan Patrick listens as Gov. Greg Abbott speaks during a roundtable about safety in Texas schools. (Ana Ramirez/Austin American-Statesman) 5 / 5Gov. Greg Abbott hosts a roundtable about safety in Texas schools at the Texas Capitol on May 22, 2018, in Austin, Texas.(Ana Ramirez / Austin American-Statesman)

After the meeting, attendees said they were surprised by the candidness of the discussion.

"It was very wide open," said Dallas ISD Superintendent Michael Hinojosa. "They didn't try to talk us into anything. They really wanted to hear what we had to say."

Hinojosa's favorite idea was implementing "assistance teams to identify these kinds of students" before they turn violent. Adding that many school districts are in a funding "crisis," he said he hopes the state will funnel more money to those already taking steps to address school safety.

"We jumped in in our master plan to try to do some things after the Florida incident, and that's going to cost our taxpayers money," Hinojosa said. "There may be an opportunity for us to get reimbursed or to have other funds they could make available. That would be very helpful."

Texas has been the site of two of the nation's worst mass shootings of the past year. In November, 26 parishioners at First Baptist Church in Sutherland Springs were gunned down during Sunday morning services by a man with a history of domestic violence. On Friday morning, a 17-year-old student at Santa Fe High School south of Houston killed eight classmates and two teachers with a shotgun and pistol he took from his father.

On Tuesday, Abbott addressed the parents of school shooters, saying, "Parents are partly responsible for this, and they need to be held accountable for it."

On Wednesday, Abbott will meet with activists on either side of the gun debate to discuss gun regulations, mental health solutions and the "underlying causes of gun violence." Invited participants include a lobbyist with the Texas State Rifle Association (the official state association of the National Rifle Association) and Rhonda Hunter, the juvenile division chief in the Dallas County District Attorney's office.

On Thursday, the governor has invited victims of shootings and their families to take part in the discussions. The list of those invitees has not been made public, but Texas Sen. Ted Cruz has said he would be attending Thursday's talks. Leaders from the Texas House and Senate, as well as education and public safety agencies, will participate in all three days, Abbott said.

When asked what gun control legislation he hopes the group discusses Wednesday, Sen. John Whitmire mentioned comprehensive background checks and closing the gun show loophole.

But is it possible to pass laws like these in red Texas?

The Houston Democrat, the longest-serving state lawmaker with a combined tenure of 45 years, said this could be the year the state passes gun regulations.

"This tragedy and other events are game changers," Whitmire said Tuesday. "I'm pretty realistic about the Capitol, but we wouldn't have had that discussion last year."

Gun regulations are rarely a serious topic for discussion in Texas. In the last few years, the state Legislature has approved "campus carry" legislation allowing concealed weapons to be carried at colleges and universities and legalized the open carry of handguns by licensed firearms owners. Texas allows churches to have armed guards and lets educators carry guns on campus if they go through training to become school marshals.

Since 2005, the state has required public schools and community colleges to have emergency plans that include live-shooter drills and safety audits at least every three years. Santa Fe High School had completed a live-shooter drill in the days before Friday's attack.

This week's gun violence meetings are closed to anyone but the invited participants.

The Texas Democratic Party criticized the governor for barring the public and the media — "Even Donald Trump kept a town hall at the White House open to press following the Parkland shootings," Deputy Executive Director Manny Garcia said.

But Abbott's staff said the meetings were kept private "to get the most comprehensive and open discussion from attendees."

On Tuesday, the governor reminded participants not to stray from their goal, and he said agreed-upon policy suggestions could be implemented through legislative or executive action.

"If you're being silent, you're not filling your seat adequately. You need to be active, engaged and focused the entire time," Abbott said. "The only thing we want to hear about are what are your ideas and about solutions that will help us to be able to reduce gun violence."

Here is the full list of Tuesday's attendees: