(CNN) An off-duty Los Angeles Police Department officer shot and killed a man who attacked him inside a Costco in Southern California while he was holding his child, authorities said.

The unidentified officer was shopping with his family in the Corona store Friday evening and holding his young child. A man he did not know "assaulted" him, said Officer Tobias Kouroubacalis of the Corona Police Department.

The officer fired his weapon, killing 32-year-old Kenneth French and injuring two of French's family members, Kouroubacalis said in a statement. The injured relatives were taken to local hospitals, where they are in critical condition, Corona police said.

Kouroubacalis described the attack as unprovoked.

The officer suffered minor injuries and has been released from the hospital. His child was not injured, Kouroubacalis said.

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