A teenage girl has been raped and burned alive in India, in the third such attack in a week in the country.

The 16-year-old girl died after being soaked in fuel and set on fire in the Sagar district of Madhya Pradesh, the BBC reported.

Police said she was killed after telling her attacker she would tell her family about the rape.

She was in her home at the time. Police have arrested a suspect, named as 28-year-old Ravi Chadhar.

Two other similar attacks occurred in India this week, both in the state of Jharkhand.

A 16-year-old girl was burned alive by a man accused of her rape, while a 17-year-old girl remains in a critical condition after being set alight by a suspect who allegedly said he wanted to marry her.

Sexual violence reports steadily rising

India approved the death penalty for child rapists following public outrage. ( AP: Rafiq Maqbool, file photo )

Reports of sexual assault of children have dominated headlines in recent weeks, leading to an outpouring of anger across the country.

Reports of sexual violence have been steadily rising in India despite the national outrage that followed the fatal gang rape of a student on a bus in New Delhi in 2012.

The incidents come less than a month after India approved the death penalty for the rape of girls younger than 12, and increased the prison term for the rape of older girls and women.

The approval of the death penalty for child rapists came after a particularly gruesome rape and murder of a Muslim girl in Jammu and Kashmir state, who was kidnapped, sedated and gang-raped in a Hindu temple.

Reported rape cases in India have climbed steadily in recent years to about 40,000 in 2016. Many more cases are believed to go unreported.

Child rape accounts for about 40 per cent of the reported cases.