(CNN) -- Police have arrested a 43-year-old former student at a small religious college in Oakland, California, in the Monday shooting spree that left seven people dead and three wounded, the city's police chief said.

The motive behind the killings at Oikos University in East Oakland remained a mystery Monday night, Oakland Police Chief Howard Jordan told reporters. Detectives had not yet questioned the suspect, and no charges had been filed, he said.

"With a case of this magnitude, with all the victims and witnesses and all the chaos, it's going to take a few days to put the pieces together," Jordan said.

Shooting witness: Teacher yelled 'run'

What is Oikos University?

Gunfire erupted inside the single-story building that houses the private Christian college about 10:30 a.m. (1:30 p.m. ET), according to Lucas Garcia, who was teaching an English class when it began. Garcia told CNN affiliate KGO-TV that he counted about six gunshots from a nearby nursing classroom when he heard someone yell, "He's got a gun."

Garcia evacuated his students from the building while the gunfire continued, he said.

The college, which caters to the Korean American Christian community, offers degrees in theology, music, nursing and Asian medicine, according to its website. Several of the victims were students, police spokeswoman Johnna Watson said.

Jordan said the relationship between the suspect and any of those shot remained unknown Monday night, as detectives processed "a very bloody scene with lots of evidence."

"Initially, we were told he was in a classroom when he stood up and began shooting at the victims," Jordan said.

Several of the survivors, including the wounded, hid behind locked doors or desks as the shooting went on. The suspect took one of the victims' cars and drove off, but surrendered to police at a Safeway grocery in the Oakland suburb of Alameda a short time later, Jordan said.

CNN's Paul Vercammen, Dan Simon and Augie Martin contributed to this report.