By Alasdair Pal

The chief minister of India's capital ordered a judge-led enquiry on Wednesday after a nine-year-old girl was allegedly raped and murdered, sparking days of protests and renewed scrutiny of the country's problem with sexual violence.

Police have alleged that the girl was killed after she had gone to fetch water from a crematorium near her house in the city's Cantonment area on Sunday. Her family told media the perpetrators cremated her body against their wishes.

Four men have been arrested in connection with the girl's murder, Ingit Pratap Singh, the top police officer in the south west of the capital where the alleged crime took place, told Reuters.

The four face charges of rape, murder and criminal intimidation, he said. They were not available for comment and Reuters was not able to determine if they had engaged lawyers.

Hundreds of people have protested since the incident, blocking roads and calling for accountability for the death.

Arvind Kejriwal, the head of Delhi's provincial government who also leads an opposition party, ordered a judicial review of the case.

He has not explained why he ordered the review but he called for the central government to act on crime and a leader of the opposition called for justice for the girl.

"Top lawyers will be engaged to get the culprits punished," Kejriwal said on Twitter.

"Central government should take strict steps to improve law and order in Delhi, we will cooperate fully."

The safety of women and girls has been a major political issue in India since the 2012 gang-rape and murder of a 23-year-old student on a bus in Delhi shocked the world.

There were more than 32,000 rapes recorded in India in 2019 according to the latest government data - almost four an hour - though experts say those figures are likely to be very conservative due to the stigma involved.

There were more than 100,000 kidnappings of women, data show, a third of them with the aim of forcing them into marriage.

Rahul Gandhi, a leader of the main opposition Congress party, visited the girl's family on Wednesday.

"Her parents' tears are saying only one thing - their daughter, the daughter of this country, deserves justice," Gandhi said.