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.
In parliament, politicians on Monday 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.
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.
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.
If you or someone you know is impacted by sexual assault, family or domestic violence, call 1800RESPECT on 1800 737 732 or visit 1800RESPECT.org.au. In an emergency, call 000.