AUSTIN (CBSDFW.COM/AP) — Texas Gov. Greg Abbott convened the first in a series of discussions on school safety Tuesday, declaring in response to last week’s shooting at Santa Fe High School, “We all want guns out of the hands of people who would try to murder our children.”

The governor called the meetings after the attack at the school located about 35 miles southeast Houston, where eight students and two teachers were slain Friday in an art classroom. The initial gathering involved school districts that arm some teachers or hire local police for security.

Abbott planned to talk Wednesday with gun-rights advocates and gun-control groups, followed Thursday by meetings with survivors of the Santa Fe shooting and the November assault on a church in the rural village of Sutherland Springs, where more than two dozen worshippers were killed.

Members of the public interested in sharing their opinion on how to improve school safety can click here.

The Republican governor has been a staunch supporter of gun rights, and there has been little mention of any new weapons restrictions in Texas, where more than 1.2 million people are licensed to carry handguns and state law allows for the open possession of rifles. The state’s top GOP leaders have instead called for “hardening” school campuses and arming more teachers.

“Every time there’s a shooting, everyone wants to talk about what the problem is,” Abbott said before the meeting was closed to the media. “By now, we know what the problem is. The problem is innocent people are being shot. That must be stopped.”

The Santa Fe High gunman used a handgun and a shotgun that were owned by his father, police have said. It’s unclear whether the suspect’s father was aware that his son had taken the weapons.

“The reality is we all want guns out of the hands of people who would try to murder our children. The question is, what are we, the leaders of Texas, going to do to prevent this from happening again?” the governor said.

One gun-control group, Texas Gun Sense, said it will push this week for tougher background checks on gun purchases, suicide-prevention programs, gun safety at home and so-called “red flag” laws that restrict gun access for people identified as potentially dangerous.

“We can’t do gun violence prevention without being optimistic. We are glad the governor invited us,” said Gyl Switzer, executive director of Texas Gun Sense. “We need immediate action. School starts in the fall, and we can’t be fooling around.”

The Texas State Rifle Association, which has played a key role in getting state lawmakers to relax gun licensing and passing open-carry laws in recent years, dismissed a call for new gun restrictions.

Alice Tripp, the rifle association’s legislative director, said the guns used in the Santa Fe attack are common in many Texas homes.

“That’s about as basic of a firearm as you can possible get. Assigning blame to a particular firearm or a caliber, that’s not helpful. You’ve got to look at whatever is that happened and see what failed,” Tripp said.

Lt. Gov. Dan Patrick said Texas should consider limiting school access, perhaps by reducing the number of entrances and arming more teachers, which is already allowed under Texas law.

After the 2012 assault on Sandy Hook Elementary School in Connecticut, Texas allowed teachers or school employees to carry handguns on campus if they met certain training requirements. Some large school districts also have their own law enforcement offices, and some others contract with local authorities for security.

Nearly 200 Texas school districts allow staff to carry guns. Santa Fe recently joined them, but officials have said the district was still in training. The school had two armed officers on campus when the shooting started. The Galveston County sheriff has said more than 200 officers responded to the emergency calls and the first “engaged” the shooter within four minutes.

The Texas reaction to the Santa Fe shooting stands in sharp contrast to the response after the Feb. 14 shooting rampage at a high school in Parkland, Florida, that killed 17 people. Three weeks after the bloodbath, Florida politicians defied the NRA and passed a gun-control package after a lobbying campaign led by student survivors of the attack.

A handful of lawmakers have called on Abbott to convene a special legislative session to address school safety. The Legislature isn’t scheduled to meet until January.

(© Copyright 2018 CBS Broadcasting Inc. All Rights Reserved. The Associated Press contributed to this report.)