"The video is disturbing," Smith said at a briefing with reporters late Sunday night. "It's disturbing any time anyone loses their life. It's a tragedy."
Smith said at least one of the officers was also wearing a body camera.
Police did not release the man's name or give any other identifying details, and Smith said he did not know whether the man was homeless.
The shooting is the latest in a recent series of fatal police shootings in Missouri, New York and elsewhere around the country that have drawn widespread protest, including the killing of a homeless man in Albuquerque, New Mexico in March, a shooting in Los Angeles in August and migrant worker in Pasco, Washington on Feb. 10.
The confrontation was caught on video, and posted on Facebook, according to the Los Angeles Times. The four-minute video shows at least five police officers getting into a scuffle with a man near a row of what appear to be blue tents.
In the video a man is heard shouting what sounds like “Drop the gun. Drop the gun.”
Then, about 25 seconds into the video, according to the counter on the video, five gunshots are heard. The video was viewed 2.5 million times within seven hours after posting.
Yoland Young, a witness, told KTLA that the victim "had three Tasers on him” during the confrontation.
“He was down but then he jumped up, like he was juiced up, and then he started swinging at the police and they were fighting him back. … They shot him five times,” Young told the television station.
Witnesses told the Los Angeles Times that the man was known on the street in the area as "Africa," and that he had been there for four or five months.
Witnesses said five or six officers were involved in the struggle, and two of them broke away to handcuff a woman who had picked up one of their dropped batons as the others wrestled the man to the ground.
One witness, Jose Gil, 38, told the Times he saw the man swinging at police then heard one of them shout, "he's got my gun!" before multiple shots were fired.
According to the Times, Dennis Horne, 29, said the man had been fighting with someone else in his tent before officers arrived.
"It's sad," Horne said. "There's no justification to take somebody's life."
The newspaper reported that another witness “who asked not to be identified, said the man punched and kicked the officers and reached for one of their service weapons before the officers fired at least seven times.”
Los Angeles Police Commission President Steve Soboroff told the Times that the LAPD, the independent inspector general and the district attorney would all investigate the shooting "very, very carefully."
Soboroff told the Times “a key issue would be whether the man did in fact try to grab the officer's gun, as some witnesses have told reporters. Otherwise, he said, it's unclear what might have prompted the use of deadly force."
"To me, that would be the only explanation that something would happen that quickly," Soboroff said. "It escalated. It escalated right in front of our eyes."
Earl Ofari Hutchinson, head of the activist group the Los Angeles Urban Policy Roundtable, called on the Police Commission to hold special hearing on use of force by officers in Skid Row encounters.
Tents and cardboard shelters cover the sidewalks of Skid Row, the downtown neighborhood where an estimated 1,700 homeless people live. Many of them struggle with mental illness and addiction.
Hutchinson said in a statement that the shooting "underscores the need for the police commission to hold a special hearing to fully examine police tactics and training in the use of deadly force by LAPD officers involving skid row residents many of whom have major mental challenges."
The violence Sunday had echoes of the August shooting by Los Angeles police of 25-year-old Ezell Ford, whose death in a struggle with officers brought demonstrations in the city.
Ford was unarmed, but police officers said he was shot only after reaching for an officer's gun.
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