One Goh has been named by police as the man believed to have shot dead seven people and injured three others at Oikos University in Oakland, California.
Oakland police chief Howard Jordan said the gunman had opened fire in a classroom at Oikos University.
The 43-year-old suspect, a former student at the college, surrendered at a supermarket in nearby Alameda city.
Oikos University is a private religious institution offering courses in theology, music and nursing.
Armed officers swarmed the college after Monday’s mid-morning attack. Five people were pronounced dead at the scene and two others died in hospital.
Bodies covered with tarpaulin were laid outside, and TV footage showed wounded people emerging from buildings.
One Goh is believed to be an Oakland resident, Howard Jordan said during Monday evening’s press conference.
He estimated it would take a few days “to put the pieces together”, adding: “We do not have a motive.”
The gunman had opened fire throughout the building, leaving a “very bloody scene”, Howard Jordan told reporters.
“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.”
The Oakland Fire Department was notified of the shooting at about 10:30 local time.
Pastor Jong Kim, who founded the school about 10 years ago, told the Oakland Tribune that the suspect was a former nursing student at the college.
He said he had heard about 30 gunshots in the building, adding: “I stayed in my office.”
A witness, Brian Snow, told local news station KGO-TV: “One of the people who was inside the building, she was saying there is a crazy guy inside.
“She did say someone got shot in the chest right next to her before she got taken off in an ambulance.”
Passer-by Angie Johnson told the San Francisco Chronicle she had helped a woman with a gunshot wound in her arm.
The woman “had a hole in her right arm the size of a silver dollar with blood coming down,” Angie Johnson told the newspaper.
She said that, according to the woman she helped, the gunman had stood up during a nursing class, shot one student in the chest at point blank range and then began firing at the rest of the room.
Reports earlier described the suspect as a Korean man in his 40’s, with heavy build and wearing khaki clothes.
A memorial service has been scheduled for 18:00 local time on Tuesday.
California Governor Jerry Brown said in a statement the shooting was “shocking and sad”.
“Our thoughts and prayers go out to the victims, their families and friends and the entire community affected by this senseless act of violence.”
The attack comes after an Ohio high school student opened fire on fellow students in February, killing three and injuring six.