The elected official, Cynthia Gonzalez, received backlash in response to the video that was posted on social media last month.
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She addressed the controversy during a City Council meeting Tuesday night.
"The message was not about violence. It was about regular people - us... claiming ownership of our streets in a time of great distress, and asking others, who I mentioned in my video... in organizing and protesting against the harm, and violence being inflicted on our community," she said.
The video has since been deleted. The Los Angeles Police Protective League has called for her resignation.