Sergeant Mmako Mophiring said both vehicles caught fire after they collided Monday on a road in central Free State.
Some victims were burned beyond recognition.
The police spokesman said Tuesday that it appeared the car was trying to overtake another vehicle when it smashed into the oncoming taxi. All four people in the car and 15 in the taxi died at the scene. Nine injured have been hospitalized.
The Road Traffic Management Corporation said reckless overtaking was one of the main causes for more than 800 deaths that have occurred on South African roads since Dec. 1.