Activists of 'Goondagardi Virodhi Sanghtan' sat outside the kotwali police station to protest against delay in tracing the girl and arrest of the accused youth.
"In wake of police inaction we have decided to sit on a hunger protest till Dusshera," group's convener Shivenderpal Singh said.
Family of the 15-year-old girl, who was allegedly kidnapped on September 24, had earlier demanded proper police action into the case.
No arrests have been made in the case so far and police have claimed that the girl had eloped with the youth.