Hundreds of Indian protesters have taken to the streets as public anger grew over the brutal gang rape and murder of a female veterinary doctor, with one politician calling for the perpetrators to be "lynched".

Four men deflated a tyre on the woman's moped and lured her to a truck yard with the promise of fixing it in the outskirts of Hyderabad in southern India on Wednesday evening.

Police say that the men then raped and murdered her before setting her body on fire with petrol under an isolated bridge.

Sexual violence against women is rife in India, and the latest case recalled the national and international outrage over the gang rape and murder of a woman by six men on a Delhi bus in 2012.

The protests today saw demonstrators brandish placards with slogans such as "We want justice". Some covered their mouths with black cloth, demanding that the government provide security and punish the guilty.

Sexual violence against women is rife in India

"I am outraged because I don't want to live with that fear," said Kawalpreet Kaur, a student at the New Delhi rally. Other marches are expected later today, including in the eastern city of Kolkata.

On Saturday, police used force to disperse hundreds of protesters after they tried to storm into a police station in Hyderabad where the four accused were held. They have since been charged.

In parliament, politicians also expressed their anguish, with Jaya Bachchan, a former actress and now an MP, saying the perpetrators should be "brought out in public and lynched".

Another member demanded a sex offenders' registry and that rapists be castrated, as others blamed the immense backlog of cases in the Indian legal system for the rise in sexual violence.

Separately, in Rajasthan in the west, a 40-year-old man was arrested following the discovery of a six-year-old girl's body a day after she went missing from her school.

Investigators said the preliminary report suggests that she was raped and beaten to death.

"We are questioning (the suspect) after locals saw him with the girl near the school before she disappeared," said local police officer, Ram Krishan.

More than 33,000 rapes were reported in India in 2017, according to the latest government figures that included more than 10,000 minor victims.