The suspected shooter, who was in custody, also had explosive devices, including a molotov cocktail, that were found in the school and nearby, said Gov. Greg Abbott, who called the assault "one of the most heinous attacks that we've ever seen in the history of Texas schools."
"We need to do more than just pray for the victims. Beginning immediately, I'm going to be working with the Texas legislature to begin discussions on taking actions," the governor said at a press conference.
Authorities identified the suspect as 17-year-old Dimitrios Pagourtzis and released his booking photo. Galveston County sheriff's officials said he is being charged with capital murder without bond.
During a brief arraignment, the suspect hung his head low and answered "yes, sir," as his rights were read to him in court. He was wearing what appeared to be a dark prison jumpsuit with his hands shackled.
Santa Fe High School student after shooting: 'Eventually it was going to happen here'
Of the 10 victims killed, one was a teacher and nine were students, officials said.
Santa Fe High School Shooting Victims: Here's what we know
At one hospital in the Santa Fe area, about 30 miles southeast of Houston, eight victims were treated and six were released. One was listed in critical condition and the other in fair condition.
Among the victims are Cynthia Tisdale, a teacher's aide, exchange student Sabika Sheika and student Chris Stone.
According to Abbott, the gunman intended to kill himself but "didn't have the courage" and instead surrendered to authorities.
Witnesses said the shooting took place in an art class on campus between 7:30 a.m. to 7:45 a.m. Students then pulled the fire alarm to alert everyone.
Teachers told their students to run, and that's when police arrived. One student said the gunman walked into a class and started shooting. The student said she saw one girl with blood on her leg as the class evacuated the room.
In an interview, a reporter asked student Paige Curry: "Was there a part of you that was, like, 'This isn't real, this would not happen at my school'?"
VIDEO: Students escorted out by law enforcement
"No, there wasn't," she said. "It's been happening everywhere. I've always kind of felt like eventually it was going to happen here, too. So, I don't know. I wasn't surprised, I was just scared."
Law enforcement officials said the school had two officers that went in to confront the suspect, and one of them was wounded.
The suspect, Pagourtzis, is a member of both the Santa Fe High School junior varsity football team and a dance squad at a local Greek Orthodox church. A few weeks prior to the shooting, Pagourtzis apparently posted disturbing images on his social media accounts, including a picture of a T-shirt that says "born to kill."
Abbott said the shooter used a shotgun and a .38-revolver in the shooting, adding that they were obtained from his father, the legal owner of the firearms. It was unclear if the father knew his son had taken the weapons. Police said the suspect also had explosive devices, including a molotov cocktail, that were found in and around the school.
RELATED: Survivor speaks about being shot in head at Santa Fe High School
Besides Pagourtzis, "one or two" other people were into custody and being interviewed as persons of interest in the case, the governor said.
The shooting was all but certain to re-ignite the national debate over gun regulations. While cable news channels carried hours of live coverage, survivors of the Feb. 14 attack in Parkland, Florida, took to social media to express grief and outrage.
Santa Fe High, you didn’t deserve this. You deserve peace all your lives, not just after a tombstone saying that is put over you. You deserve more than Thoughts and Prayers, and after supporting us by walking out we will be there to support you by raising up your voices.— Emma González (@Emma4Change) May 18, 2018
"We are fighting for you," David Hogg, a survivor of the Feb. 14 attack in Parkland, Florida, said on Twitter. He added: "Get ready for two weeks of media coverage of politicians acting like they give a s--- when in reality they just want to boost their approval ratings before midterms."
Fellow Parkland student Emma Gonzalez also tweeted: "Santa Fe High, you didn't deserve this. You deserve peace all your lives, not just after a tombstone saying that is put over you. You deserve more than Thoughts and Prayers, and after supporting us by walking out we will be there to support you by raising up your voices."
WATCH: Student's first-person witness account
KTRK and the Associated Press contributed to this report.