The incident took place Saturday in Shankargarh locality in Allahabad, about 230 km from here, Saturday. Police swung into action late Sunday after women's groups protested inaction.
Mohit Agarwal, senior superintendent of police in Allahabad, said teams were looking for the alleged attacker, 20-year-old Gyan Patel, and his parents.
The girl, who is battling death with more than 70 percent burns, has been admitted to a city medical facility, an official said.
Police have lodged a first information report (FIR) and are conducting raids to arrest the assailant and his parents, who allegedly connived in the crime. An official said the girl has three sisters and is a Class 10 student at a local inter college. Her father is a vegetable vendor.
Giving details of the crime, an official said the teenager was alone at home when Patel barged into the hutment and tried to force himself on her. The girl fought him back bravely and managed to foil the rape bid.
Patel then fled the scene, only to return with his father Santosh Patel and mother Geeta. They then doused the unsuspecting girl in kerosene and set her on fire, police said.
Her sisters, who had gone to bring water from a nearby well, saw smoke coming out from their house and rushed back to see their younger sister was burning. They managed to douse the flames but not before the girl was severely burnt.
Neighbours called in an ambulance, which rushed her to a hospital where her condition is stated to be serious. Senior police officials swung into action only after local social worker Manju Pathak intervened Sunday afternoon.
Superintendent of Police (Crime) Arun Pandey went to the hospital and recorded the statement of the girl who narrated the horrifying act of the neighbour.
She also said Patel warned her against going to the police, saying he would contest the case by selling off his agriculture land and tractor whereas she would lose the case.