The man, thought to be in his 30s, was found bleeding from several stab wounds to his chest with his three sons dead in the back of the car.
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The children, aged between eight and 12, were already dead when police arrived at the scene in Los Angeles, US.
A knife was found on the passenger seat.
A senior officer said the discovery was so horrific it "scarred" the cops who found the bodies.
The father, whose name has not been released, is the only suspect in the killings, police said.
He was taken to a hospital in critical condition and will be arrested if he survives his wounds, Los Angeles police officer Matthew Ludwig said.
Mourners mounted a prayer vigil outside the Dolores Huerta Elementary, in downtown Los Angeles, on to honour the boys.
Candles, flowers and photographs of the victims were left, with the messages “We love you!” and “Rest in peace.”
Cards named them as Juan, Alex and Luis, reports the Guardian.
The motive behind the killings is unclear and is being investigated.
The father had no history of domestic violence charges or arrests, police said
Mr Beck said the boys' mother is deceased and that their stepmother was safe and being interviewed by detectives.