The SUV is registered in the name of a relative of Sena leader Pappu Mane, who often uses it, but was not inside the vehicle at the time of the mishap that occurred on the Baramati-Morgaon road, 120km from Pune, a senior police official said.
Following the accident, the driver and other occupants of the SUV fled from the spot, leaving behind the vehicle. A group of angry locals set it on fire and resorted to a 'rasta roko' (road block) to demand the driver's arrest, he said.
The deceased girls, identified as Samiksha Vitkar (13) and Divya Pawar (12), were on their way to school when they were knocked down by the car.
"According to our investigation, there were three to four people inside the car when the accident took place, but Mr Mane was not inside the SUV. We have summoned him for questioning," he said.
The law and order situation in the area is under control, the police added.