The girls' mother, who was estranged from their father, called police Sunday afternoon and reported that the man had kidnapped the girls, The Local.ch reported.
Police said he fled with the girls in his car.
A manhunt for the man was launched before police received a report of a burning car in a forest clearing in the Simmenbodeli area of Saint Gallen, near Grabs.
At the scene of car fire, police found the bodies of the children. The girls' father was found a several hundred feet away suffering from serious burns.
The man was flown to a hospital where he later died.
Police said they have not yet determined how the girls died, but they have ruled out an accident.
"We assume that the man burned the car," police spokesman Peter Krusi told Blick.ch on Monday.
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