As protests and vigils spread to other parts of the country, Prime Minister Manmohan Singh described the attack as a "heinous crime" and said he was directing the Government to take steps to try to protect women.
The Home Ministry said extra police patrols and fast-track courts were being set up and opposition MPs joined hundreds of others to demand what campaigners called a change of mind-set and culture.
The student and her companion were attacked with iron rods by the six men who were driving a bus around the city and stopped to pick up the pair, who thought it was a regular public transport vehicle.
After driving through police checkpoints over several hours while the woman was repeatedly raped, the men stripped the pair and dumped them by the side of the road.
Sonia Gandhi, head of the ruling Congress Party, visited the woman in hospital and claimed there would be swift action taken against the perpetrators. She also called for police to be trained to deal with crimes against women.
Hospital officials said the woman has been able to write a message to her family in Uttar Pradesh.
"It is a matter of shame that these incidents recur with painful regularity and that our daughters, sisters and mothers are unsafe in our capital city," Gandhi wrote to New Delhi Chief Minister Sheila Dikshit, whose house was besieged by protesters.
Large parts of northern India, where patriarchal attitudes dominate, have a wretched reputation for offences against women. Campaigners say that very often victims do not report attacks out of fear of dealing with the police or the legal authorities. Senior police officers have often blamed the victims, citing the way they were dressed or that they dared to be out at night.
Women from some of the city's poorest neighbourhoods joined students and other demonstrators at the India Gate memorial to demand the Government take action. Some carried banners demanding that the attackers be hanged publicly or castrated.
"I feel this attack in my heart. I am a woman, I have to deal with sexual harassment," said Ramzan, 55, who has four children.
Asked if such harassment happened often, another woman, Kalavati, said: "It happens everywhere - at the police station, in the hospital, in the market, in the street."
Police say five of the six men allegedly involved in the attack have been detained and the search is continuing for the other one.
Yesterday some of the accused appeared in court. According to the Press Trust of India, one of them, Pawan Gupta, said: "I accept I am guilty, I should be hanged."
- Independent
