A 15-year-old girl was fighting for her life in a New Delhi hospital on Tuesday after being raped and set on fire on the rooftop terrace of her family's home in a village outside the city, police said.

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.

In the latest case, police arrested a 20-year-old man for allegedly raping and attempting to burn the girl to death on Monday in Tigri village, near the New Delhi suburb of Noida in the state of Uttar Pradesh, according to Yadram Singh, of the Bisrakh police station.

Police fire water cannon at India rape protesters

Singh said the man "had severe burns on his hands" and was charged with several offences, including rape, attempted murder, assault of a minor, and causing grievous injury.

The girl was in critical condition in a New Delhi hospital, Singh said. Indian newspapers reported that she suffered burns on 95 percent of her body.

Singh's police report on the case describes how the girl's parents found her after hearing her screaming from the rooftop terrace a few hours before dawn Monday.

The girl later told police that she was raped, beaten, and then set on fire by a man who she said had been stalking her for months, Singh said.

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.

OPINION: Rape and the Indian male

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.