White recently had been involuntarily committed and later released in another city, according to Carter, who provided no other details.
Armed with a "bowie-style" hunting knife, the suspect "calmly walked around" campus Monday afternoon and randomly stabbed other students, police and witnesses said. White, who was booked on a murder charge, will face additional counts, authorities said.
The stabbing attack does not appear to be part of a larger assault, though authorities were still trying to determine a motive.
"This was not a conspiracy," Carter said. "This was not about a person who had a vendetta."
Austin Police Chief Brian Manley added, "There is no evidence linking this to any part of a larger plan."
The student killed Monday was identified Harrison Brown, a freshman who hoped to have a career in music, said university president Gregory L. Fenves.
"His family and our community will never be able to hear Harrison play and sing again and, for this, our hearts are breaking and we are deeply deeply saddened," Fenves said.
Fenves met with the victim's family on Tuesday.
"It was an incredibly difficult time for them -- unimaginable," he said. "Mrs. Brown talked about her son Harrison and how much he loved being a Longhorn in his first year here."
Two hours after the attack, classes and events were canceled for the rest of the day but activities resumed on campus Tuesday amid what Fenves described as "a great deal of fear on campus and in our community."
"We are in mourning and we are hurting as a university community," Fenves said.
The first person attacked was one of several students gathered around a popular Austin food truck around 2 p.m. at the plaza outside Gregory Gym, one of the busiest areas on the 431-acre campus.
Rachel Pritchett, a freshman, was in line at the food truck when she heard someone screaming.
"I didn't really process what was happening until he grabbed this guy who was standing right next to me by the shoulder and stabbed him on the back," she told CNN affiliate KEYE.
"While I was running away, I saw this other guy that was kind of bloodied up sitting at a table slumped over. There was someone standing next to him yelling, 'get away!'" she said.
Students leaving their classes also walked upon a gruesome scene.
"Police were resuscitating a victim. Another student had lacerations to their head and was getting help from police," said student Ray Arredondo.
As the attack unfolded, three other students were hurt before police arrived.
"I looked over towards the Gregory Gym area and I just see somebody like passed out on the floor covered in blood," student Bryan Ramirez told CNN affiliate KXAN.
Two students were released from the hospital later Monday.
A chaotic scene
Responding to the 1:49 p.m. call about a stabbing, campus police saw the suspect walking away from a person lying on the ground, Carter said.
When he was confronted by police, the suspect offered no resistance and complied with the officer's order to get on the ground, Carter said.
Witnesses say he had a "nonchalant" look on his face.
Campus, local and state police swarmed to the plaza. They helped the injured and placed yellow-tape barriers as students called their loved ones.
"There are no words to describe my sense of loss," Fenves said in a message sent to students, faculty and staff.
'A great deal of fear on campus'
Authorities do not believe there is an ongoing threat to the campus community but have increased patrols as a precaution.
"Campus safety is our priority and we will investigate this tragic incident to the greatest extent possible," Fenves said.
In another message, Fenves urged students and staff to support the victims and reassured them that there were no ongoing threats on campus.
"There is a great deal of fear on campus and in our community. That fear is very understandable, especially in light of recent vandalism and threats against students," he said.
Monday's attack comes about a year after the slaying of 18-year-old student Haruka Weiser.
The theater and dance student was walking home from class when she was strangled and sexually assaulted. Meechaiel Criner is awaiting trial on charges of capital murder in her death.
Weiser's case was UT's first on-campus homicide investigation since 1966.