An Indian teenager was gang-raped in two separate attacks and then died after being set on fire, sparking protests in the eastern city of Kolkata, police said on Thursday.

The 16-year-old was assaulted first on October 26 and then again the day after by a group of more than six men near her family's home in Madhyagram town, about 25 kilometres (15 miles) north of Kolkata.

The second rape occurred as she was returning home after reporting the first attack at a police station.

She was then set on fire on December 23 and died in a state-run hospital late on New Year's Eve, police said.

"She gave us a dying declaration in front of the health officials that she was set on fire by two persons close to the accused when she was alone at home on December 23," local policeman Nimbala Santosh Uttamrao told AFP.

Police made their first arrests on Wednesday, two months after the initial crime, local police chief Rajiv Kumar told AFP.

"The accused tried to kill my daughter by setting her on fire to hush up their crimes," the victim's father, a migrant taxi driver from India's poorest state Bihar, told AFP.

Neither he nor the victim can be named for legal reasons.

Several hundred activists on Wednesday protested in Kolkata over the crime, which was shocking in its brutality, even after a year when sex crimes have been widely reported in India.

Rampant rape, assault and harassment of women in India was in the spotlight in the past 12 months after the fatal gang-rape of a 23-year-old student on a moving bus in New Delhi in December 2012 sparked nationwide outrage.

The parliament has since passed tougher laws to punish rapists.

Activists say rape victims in India often face severe threats and intimidation from their attackers after the assault, while police often discourage them from lodging complaints.