KVUE-TV reports that Austin police had one person - identified as Kendrex White - in custody after the Monday afternoon stabbing.
Cater says the attacker did not resist when officers ordered him to the ground at gunpoint.
A police report said the injuries were not life-threatening.
"He [White] walked a little ways, stabbed someone, and then walked a little ways and stabbed another", Carter said.
The suspect is a UT student and is in custody, campus police said.
Krishant Dania, psychology and government freshman, said he was sitting outside of Gregory Gym when he saw one of the victims and ran over to help.
The motive for the attack remains under investigation, but Carter said at a Tuesday press conference that White had previously been involuntarily committed in another city for mental health issues.
Kendrex White is the accused culprit behind the May 1 mass stabbing at University of Texas Austin that left at least one dead. The authorities did not immediately release the victims' names. Police said the injured victims were either 20 or 21.
"It didn't seem real", Garza said in an interview with ABC News on Monday.
"That's a really busy area of campus where lots of food trucks come to sell food to students during lunch".
Stabbing on University of Texas at Austin campus on May 1, 2017.
Another student, Ray Arredondo, said he was walking to his vehicle when a mass of students near the gym started running.
"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. He was ultimately shot dead by police. With the rumors and second attack so close to their homes, and in light of recent graffiti attacks on their houses in recent weeks, multiple Greek fraternities and sororities took extra steps to make sure their members were safe Monday. The suspect, who was brandishing a long knife, then entered a dormitory building where he was arrested by officers as he approached other students.
No one was injured, and police said neither the shooter or his target were affiliated with the university. "I have been briefed by the Department of Public Safety on both incidents, and have also talked to University of Texas at Austin President Greg Fenves". Group President Melody Adindu said White was passionate about his work and was "very interactive and easygoing". His Twitter profile indicates he is a junior biology-premed major from Killeen, Texas. "He was always nice, had plenty of friends". "I'm definitely surprised", said KHS grad Kay'Lynn Wilkerson, who attends Sam Houston State University in Huntsville.
Former classmate Angela Bonilla described White as "the sweetest guy", while others remembered him similarly. White apparently got into a crash when he failed to yield to the right of way when he turned a street corner - and after police confronted him, he admitted to consuming two "happy pills", which were later listed as Zoloft, according to the news station.
Carter says the campus siren system wasn't used because that would indicate the need for a lockdown.