Police who arrived at the scene in a working class neighborhood dotted by tall palm trees found shell casings and blood throughout the restaurant, located west of downtown Los Angeles.
Two possible suspects were being questioned.
Los Angeles Police Department Officer Mike Lopez said a preliminary investigation found a party was underway at 12:30 am today in the restaurant, operating out of a converted home, when an argument started.
A man and woman left, then returned, and the restaurant erupted in gunfire.
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He called it "the latest example of a senseless gun violence epidemic that causes so much pain and sorrow in our city and across the nation.
"We cannot tolerate these tragedies multiplying in communities across America," Garcetti said in a statement.
The shooting occurred in a residential area of modest homes. Investigators were snapping photographs and scouring the ground in an area that extended over two blocks.
Three people died at the scene, and 12 others were transported to local hospitals. Their conditions ranged from critical to stable but serious.
"There was some type of party there," Lopez said. After the couple left the restaurant and returned "that's when the shooting occurred."
Neighbor Sheryl Cobb said she was awakened by screaming and gunfire, but never left her home for fear of getting caught in a crossfire.
"Bullets don't have names on them," she said. LAPD Sgt. Frank Preciado told The Los Angeles Times (https://bsmedia.business-standard.comlat.Ms/2diVuqZ ) that the restaurant was "a bloody scene with shell casings everywhere." One firearm was recovered.
The Times described the restaurant as a popular Jamaican eatery that features a DJ yesterday night.