Olga Tyurina (29) and Irina Babayan (25) were returning from a discotheque at Saligao in North Goa after attending Christmas party on Thursday, Dec 24.
Both girls filed their complaint at Anjuna police station.
The complaint said they had to jump out of the taxi to escape from his clutches and hide in the woods for almost five hours waiting for the dawn.
The taxi driver who initially had agreed for Rs 300 took them by another road pretending to avoid police picketing at 2:20 am. He stopped at Anjuna beach and demanded Rs 1,000 instead, they said.
"When we protested, he tried to grab us. We were horrified and jumped out of the taxi and took shelter in the woods nearby," they said.