Activists in a San Diego suburb Wednesday called for a federal investigation into the police killing of an unarmed black man who relatives said was mentally ill.

"We do not trust local prosecutors to investigate local police," the Reverend Shane Harris said at a press conference, according to the Los Angeles Times.

Police in El Cajon said they responded to a call Tuesday afternoon about a man behaving erratically and shot him after he appeared to pull something from his pocket and point it at police officers.

The man was identified as Alfred Olango, 30, local news media reported, citing relatives and demonstrators who took to the streets in protest.

A woman identified as the man's sister said he was mentally ill and that she had called police for help.

"I just called for help and you killed him," she said in a video of the aftermath of the shooting posted on YouTube.

A witness filmed the incident and has turned the video over to police, police said. They later released a still image from the video showing two police officers pointing weapons at a man in a shooting stance.

Police said they had recovered the object he was holding but did not disclose what it was, according to news reports.

A Facebook page for the man said he was originally from Uganda, the Los Angeles Times reported. A relative of the man, Agnes Hassan, told reporters the two had been in a refugee camp together before coming to the United States.

Live news video showed a crowd of several dozen protesters gathering at an intersection in El Cajon chanting "black lives matter." One demonstrator carried a sign that read "stop racist police terror."

The suburb is 16 kilometres east of San Diego in southern California.

The fatal shooting follows police killings of black men in Tulsa and Charlotte, which sparked widespread protests.

Olango was at least the 716th person shot and killed by police in the US in 2016, according to the Washington Post.

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