OAKLAND police chief Howard Jordan has identified the suspect as One L Goh after seven people were killed and three more were injured at a small Christian university in California.
Speaking at a news conference Mr Jordan said: "Preliminary investigation led to the identity of the suspect. 43-year old One L Goh.... His description [led us to believe] that he had fled the area most likely before the first officers arrived," Mr Jordan said.
He added that the shooter, who opened fire in a classroom at Oikos University, appeared to have acted alone and was now in police custody.
Former nursing student Goh surrendered at a supermarket in nearby Alameda city after allegedly opening fire in a classroom, killing seven people and injuring three others.
The khaki-clad Korean American remained on the loose for nearly two hours before allegedly walking into a Safeway supermarket and announcing to staff at the customer service desk: "I just shot some people."
The police chief said that it would still take a few days to investigate the shooting and find out a motive. But he described a violent scene from the shooting.
"Officers found several victims throughout the classroom, throughout the building," he said.
"There were several people hiding in locked buildings, locked doors behind desks, as you can imagine, very frightened, very scared.
"Some of them were injured so we had to rescue them out. We had to force our way into a number of rooms."
Oikos University is a private Christian college offering courses in theology, music and nursing.
The attack took place in a lecture room where a nursing class was being held at the $25,000 a-year (€18,750) Oikos University, in East Oakland, California, at 10.33am local time.
The college is popular with students from the Roman Catholic Korean community, and the gunman was said to have been enrolled on a nursing course at one point but had stopped attending classes.
Four bodies could be seen covered by tarpaulins on lawns in front of the school, while rescue workers removed other casualties from inside the building on stretchers. Nearby Highland Hospital said it had treated four victims, one of whom is thought to have died of their wounds soon after the incident. Others were still being taken out of the university hours after the shooting stopped.
Students were ordered to leave the building in ones and twos over the space of an hour as a police SWAT team took positions before smashing their way in through windows and doors using a sledgehammer.
A witness, Angie Johnson, 52, of San Leandro, said she saw a young woman run out of the university with blood pouring from her arm, crying: “I’ve been shot, I’ve been shot.”
Mrs Johnson said she waited with the woman for medical help to arrive, and was told that the gunman was a man in her nursing class who stood up and shot one person at point-blank range in the chest before spraying the room with bullets.
“She said he looked crazy all the time,” Mrs Johnson said. “But they never knew how far he would go.”
The victim “had a hole in her right arm the size of a silver dollar with blood coming down”, she added.
In a statement, Cynthia Perkins, a public safety official, said: "Ten people were injured during this morning's shooting, seven of which are fatalities."
According to its website, Oikos offers classes in religious studies, music and vocational nursing, and caters particularly to students of Korean descent.