A teenager, who was raped before she was set on fire on the roof of her family's home, has died of her injuries in a New Delhi hospital, police said.

The 16-year-old had been fighting for her life after suffering more than 90 percent burns in Monday's attack, which occured in a village outside the capital.

"Unfortunately, she could not be saved despite the best efforts of the medical staff," Ashwani Kumar, an investigating officer told the AFP news agency on Wednesday.

He also confirmed the arrest of a 19-year-old man who is suspected of carrying out the attack.

"We have arrested the accused, who is 19 years old and sent him to judicial custody," he said, adding that "an investigation is on to find out more about the motive and details of the crime".

The Indian paper Hindustan Times identified the suspect as Ajay Kumar and quoted police as saying that he would face murder charges.

Media reports quoted the girl's father as saying a neighbour in their village in the northern state of Uttar Pradesh had been harassing his daughter for a year despite several warnings.

The attack is just one of several recently reported cases of rape against women or children in India - underlining the persistence of such violence despite a public outcry three years ago that led to stronger laws to prevent sexual assault.

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India's women and children are considered particularly vulnerable to sexual violence and harassment because of widespread social taboos against speaking about sexual assault.

The stigma is enough to keep many from even reporting crimes, while many others face police resistance in filing complaints.

Analysts say that has started to change since the fatal gang-rape of a 23-year-old woman on a New Delhi bus in 2012 triggered national anger and demands that more be done on women's safety.

The government rushed through legislation to double prison terms for rape, and to criminalise voyeurism, stalking and the trafficking of women. But activists say more action is needed, including better education in social responsibility for youths and adding basic safety infrastructure such as street lights and public bathrooms.