Violence broke out as the protesters, mainly college students, tried to break through police barricades to march on the presidential palace.
There has been outrage in India over the attack on a bus last Sunday that has left the 23-year-old woman in a critical condition in hospital.
Six people have been arrested.
The government has tried to halt the rising anger over the attack by announcing a series of measures intended to make Delhi safer for women.
They include more police night patrols, checks on bus drivers and their assistants and the banning of buses with tinted windows or curtains.
‘Sips of water’
But the protesters say the government’s pledge to seek life sentences for the attackers is not enough – many are calling for the death penalty.
Some carried placards reading “Hang the Rapists” and “Save women. Save India” as they marched on Saturday.
Junior home minister RPN Singh appealed for calm after the clashes broke out. “This is not a way to protest,” he told India’s CNN-IBN television. “Trying to storm buildings and breaking barricades is not a way to start a dialogue.”
The woman and her friend had been to watch a film when they boarded the bus in the Munirka area intending to travel to Dwarka in south-west Delhi.
Police said she was raped for nearly an hour, both she and her companion were beaten with iron rods and thrown out of the moving bus into a Delhi street.
Doctors said on Saturday that the woman remained in a critical but stable condition, but had been removed from a ventilator.
“She is doing much better than yesterday,” said BD Athani, superintendent of Safdarjung Hospital.
The attack has prompted a week of candle-lit vigils and demonstrations amid some soul-searching about the safety of women in Delhi and other parts of the country.
Police figures show that, in Delhi, a rape is reported on average every 18 hours and some form of sexual attack every 14 hours.
Indian novelist Arundhati Roy said rape is seen as a “matter of feudal entitlement” in many parts of the country, and the reason this case had come to light is because the woman victim belongs to the affluent middle class.
She said attitudes towards women need to change in India, because a change in the law only will protect middle class women, but “the violence against other women who are not entitled will continue”.