New Delhi alone reported 572 rapes last year and more than 600 in 2012.
Six suspects, including the bus driver and a minor, have now been arrested in connection with the rape of "Damini."
As fury about the assault gathered pace, some Indian lawmakers called for treating rape as a capital crime.
"We'll work collectively to see we make a law which is deterrent and preventive," said New Delhi's chief minister, Sheila Dikshit.
India's Home Minister Sushilkumar Shinde told reporters Saturday that the government would work toward increasing punishment in "rarest of the rare" rape cases.
But pressed on whether the administration would agree to demands for death by hanging in such instances, he said: "We'll have to see in what way it (the rape sentencing) can be enhanced."
Shinde said the government was pushing for a speedy trial for the attack.
Authorities are also taking a number of steps to improve security for women in New Delhi, particularly on public transport, he said.
"(The) government shares the widespread concern and support that has been expressed throughout society for the girl who has so suffered. Government also respects the right of legitimate protest," Shinde said.
"At the same time, there is need to exercise calm at this juncture and for everyone to work together to improve the safety and security environment."
In the meantime, the victim has been promised the best possible medical care, Shinde said.
A physician described the woman's condition Saturday as better than a day earlier, but said there was still a risk of infection. She is receiving psychological as well as medical care, he said.
Following the brutal assault, the country's human rights body sent notices to city police and federal authorities, demanding an explanation.
"The incident has raised the issue of declining public confidence in the law and order machinery in the city, especially in its capacity to ensure safety of women, as a number of such incidents have been reported in the national capital in the recent past," the National Human Rights Commission said in a statement Tuesday.
Home Secretary R. K. Singh announced the suspension of five police officers in the wake of the rape.