Hundreds of Indian protestors took to the streets on Monday as public anger grew over the brutal gang-rape and murder of a female veterinary doctor, with one MP calling for the perpetrators to be "lynched".

The demonstrations in New Delhi, Hyderabad, Bangalore and elsewhere took place as police found the semi-naked body of a six-year-old girl who appears to have been raped and then strangled with her school belt in Rajasthan.

The spark for the protests was the gang-rape and murder by four men of the 27-year-old vet next to a busy road in the outskirts of Hyderabad in southern India on Wednesday evening.

The men deflated a tyre on her moped and lured her to a truck yard with the promise of fixing it. Police say that the men then raped and murdered her before setting the 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 at the gang-rape and murder of a woman by six men on a Delhi bus in 2012.

The protests on Monday 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.

"I am outraged because I don't want to live with that fear," Kawalpreet Kaur, a student at the New Delhi rally told AFP. Other marches were expected later on Monday, 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.