Officers received a call at 4:24 a.m. from a resident in the area of Bayshore Boulevard and Raymond Avenue, who said a person was threatening other tenants with a knife, San Francisco police Sgt. Lyn Tomioka said.
Responding officers found the suspect standing at the top of a stairwell with a knife to his own throat, according to Tomioka.
The officers told him to put the knife down, but he refused and told the officers they would have to shoot him, Tomioka said.
The officers employed extended range impact weapons at the suspect "with no effect," and then entered the building through the rear of the property, she said.
At that point, the officers were still talking with the suspect, but he repeatedly refused to listen to the officers' orders, Tomioka said.
Then, the suspect made a move toward the officers, and one officer fired a single round at the suspect, striking him, Tomioka said.
"He went toward the officers in a manner that the officers believed their lives were in immediate danger," she said.
The suspect was transported to San Francisco General Hospital where he was pronounced dead, she said.
Authorities are investigating the circumstances surrounding the shooting, the Police Department's first fatal officer-involved shooting this year.
"We will investigate fully and determine what was going on prior to arrival," Tomioka said.