(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.
"The Department has initiated an Administrative Investigation and is working with the Corona Police Department to learn more about the incident," Los Angeles police said in a statement.
Lt. Jeff Edwards of the Corona police told reporters just after the incident that police believed the shooting resulted from an argument.
"From my understanding, from some people we talked to, there was apparently an argument inside," Edwards said. "Some type of argument and ensued into a gun shot."
Officers arriving to the scene Friday initially believed there was an active shooter, Edwards said. Panic broke out as people tried to flee the store, leaving some injured in the scuffle.
Many left their personal items -- purses, cellphones, and backpacks -- at the store in an effort to get out quickly. Corona Police are now trying to find their rightful owners.