Indian police are investigating two separate lynchings in which men were beaten to death by frenzied crowds over alleged assaults on young women.

In the northeastern state of Nagaland, a curfew was imposed on Dimapur city after a mob dragged a rape suspect out of jail on Thursday, killing him and stringing him up from a clock tower. Another man was killed in the subsequent police firing.

Meanwhile another man was killed in a mob attack in the northern city of Varanasi after a group of girls alleged they were molested while celebrating the Hindu festival of Holi.

"The irate crowd assembled following a complaint by some young women to their families that they were molested... by a few men from that area," Anil Kumar, in charge at the local police station, told AFP.

"We are investigating into the mob violence and also ascertaining whether the deceased was one of the alleged molesters. The dead man is in his fifties and was beaten with sticks. So far, three people have been arrested."

In the Nagaland incident, the mob's victim had been arrested and jailed in late February, accused of raping a woman multiple times.

Meren Jamir, superintendent of police in Dimapur, told AFP that a 25-year-old youth suspected to be part of the mob was injured in police firing, and later succumbed to his injuries at the hospital.

He said police were "trying to bring the situation under control".

Tensions had been rising in the area since February 24 when police arrested the alleged rapist over the assault of a 19-year-old tribal woman.

Nagaland Chief Minister TR Zeliang said the suspect was a Bangladeshi immigrant, and Jamir said his killing had been followed by attacks on Bangladeshi-owned businesses.

Nagaland's indigenous tribal groups have for years accused the growing population of Bengali-speaking Muslims from nearby Bangladesh of illegally settling on their land and eating into their resources.

Jamir said the situation was "very tense", but they were trying to "restore order", with hundreds of riot police personnel patrolling the streets.

An inquiry has also been opened into the prisoner's killing, Zeliang told AFP by telephone.

"The curfew will continue until the situation improves. We will do whatever possible to stop any escalation," he said.

The violence comes as India is in the midst of a raging controversy over a government order to ban the broadcast of a documentary about the December 2012 gang-rape of a young student.

The incident, which sparked outrage both within India and around the world, highlighted the frightening level of violence against women in the world's second most populous country.