Arming more teachers could help tackle gunmen targeting students if there were "four to five guns to one", a senior Texan official has said.
Lieutenant Governor Dan Patrick was speaking two days after 10 people were killed at the Santa Fe High School, which had an armed guard.
He had previously said schools had "too many entrances and too many exits" and their design should be reconsidered.
The proposal to arm teachers is not a new idea.
After a 14 February school shooting in Florida, US President Donald Trump suggested giving teachers a bonus if they carried guns.
But he clarified via Twitter that "only the best 20% of teachers" - those with military backgrounds or special training - should be allowed guns.
Mr Patrick, a Republican, told CNN that the best way to stop a gunman was "with a gun".
"But even better than that is four to five guns to one," he said.
Hours earlier, the police chief of neighbouring Houston said he had hit "rock bottom" over failure to enact gun reforms.
Chief Art Acevedo wrote on Facebook that he had "shed tears of sadness, pain and anger" over the shooting.
The shooting was the latest in a series of deadly incidents across the US that have reignited debate about gun control.
Police now say eight students and two teachers were killed when another student opened fire in an art class shortly before 8am local time on Friday at the Santa Fe High School. Thirteen others were wounded in the attack, with two in critical condition.
Among the dead are a Pakistani exchange student and a substitute teacher.
Dimitrios Pagourtzis, 17, has been charged with murder after surrendering to police. He later admitted "to shooting multiple people". He allegedly used a shotgun and a revolver taken from his father, who legally owned the weapons.
It was the fourth deadliest shooting at a US school in modern history, and the deadliest since a student opened fire in February at Marjory Stoneman Douglas High School in Parkland, Florida, killing 17 people.
The Florida attack spawned a nationwide youth-led campaign for gun control, and a series of proposed changes, including moves to ban so-called bump stocks used in last year's Las Vegas shooting that killed 58 concert-goers.
Dan Patrick is a well-known proponent of gun ownership. He has advocated carrying weapons openly and concealed in Texas - and reiterated some of his views on Sunday, too.
He told CNN's State of the Union programme that restricting school entrances and arming more teachers could reduce such incidents.
"When you're facing someone who's an active shooter, the best way to take that shooter down is with a gun. But even better than that is four to five guns to one," Mr Patrick said.
ON ABC's This Week, he blamed a culture of violence.
"We have devalued life, whether it's through abortion, whether it's the breakup of families, through violent movies, and particularly violent video games."
Challenged over gun ownership that made it so deadly in the US - unlike in other countries that had the same social challenge - Mr Patrick said: "Guns stop crimes."
Chief Acevedo runs the police department of America's fourth most populous city, Houston, which lies nearly 64 km north-west of Santa Fe.
"I know some have strong feelings about gun rights but I want you to know I've hit rock bottom and I am not interested in your views as it pertains to this issue. Please do not post anything about guns aren't the problem and there's little we can do," Chief Acevedo said in his Facebook post.
"This isn't a time for prayers, and study and inaction, it's a time for prayers, action and the asking of God's forgiveness for our inaction (especially the elected officials that ran to the cameras today, acted in a solemn manner, called for prayers, and will once again do absolutely nothing)," he added.
In just a few hours, his post had received more than 29,000 reactions and 15,590 shares.
Chief Acevedo first spoke out about gun control in the aftermath of the Las Vegas shooting last October, and was a prominent figure in Texas's March for Our Lives demonstration following the Florida attack earlier this year.
Who are the victims?
None of the victims has yet been identified by US authorities, but family members of the victims have spoken to media outlets. The embassy of Pakistan in Washington DC confirmed that exchange student Sabika Sheikh, 17, was among the dead.
She had been on a special study abroad programme set up by the state department in the aftermath of the 11 September 2001 attacks to bring students from Muslim-majority nations to the US on a cultural exchange.
Substitute teacher Cynthia Tisdale was also killed in the attack, her family told US media outlets. Ms Tisdale's brother-in-law John Tisdale described her on Facebook as an "amazing person".
The LA Times says it has spoken to the mother of another victim, 16-year-old Shana Fisher, who she said had "had four months of problems from this boy" - referring to the gunman.
"He kept making advances on her and she repeatedly told him no," the mother Sadie Rodriguez said, adding that her daughter finally stood up to him and embarrassed him in class a week before the shooting.
The other victims who have been named by US media are:
- Jared Black, 17 - student
- Christian Garcia, 15 - student
- Aaron McLeod, 15 - student
- Ann Perkins, 64 - substitute teacher
- Angelique Ramirez, 15 - student
- Chris Stone, 17- student
- Kimberly Vaughan, no age given - student
What has happened to the attacker?
The 17-year-old suspect has been charged with capital murder and aggravated assault of a public servant.
Court documents revealed on Saturday that the suspect - who waived his right to remain silent and admitted to the shooting - told police he had spared certain students he liked "so he could have his story told".
One of his two lawyers, Nicholas Poehl, told Reuters news agency his client was "very emotional and weirdly nonemotional".
"There are aspects of it he understands and there are aspects he doesn't understand," he added.