The death of the 23-year-old woman, who has not been named, prompted street protests across India, international outrage and promises from the government of tougher punishments for offenders.
Police on Tuesday confirmed they would push for the death penalty for her attackers - the force can recommend prosecutors pursue particular punishments in Indian trials.
The physiotherapy student was raped and tortured on Dec. 16 by a group of men armed with a metal bar on a private bus in New Delhi, nicknamed India's 'rape capital'. She died from her injuries on Saturday in a Singapore hospital.
Relatives scattered the woman's remains in India's largest river, which is sacred to the Hindu religion, during a small ceremony in the district of Ballia where she was born, a senior local official told Reuters.
"The immersion of the ashes was a private affair, a family affair," said R.M. Srivastava, home secretary of Uttar Pradesh, the state where the ceremony took place.
"NEW YEAR, NEW ATTACKS"
Indian media reported a string of new attacks on Tuesday, including a woman set on fire, allegedly by a stalker, in Uttar Pradesh and another woman stabbed to death in a busy market district of eastern Delhi.
In a debate titled "New Year, New Attacks, New Rapes" on television network NDTV, lawyers and politicians from several parties promised fast action to tighten laws.
"Keep up the social pressure, socially ostracise these people," said Renuka Chowdhury, a senior member of the ruling Congress party.
Protesters braved chilly weather in New Delhi to hold candlelight vigils and small rallies on New Year's Day.
"I'm going to stand here until the government actually decides to give women some safety," one young woman told journalists. Other protesters brandished placards that read "First of January is a black day."
The attack revealed deep fissures in Indian society, where staunchly chauvinist views clash with a fast-modernising urban culture in which women play a growing role in public life.
The case also cast a spotlight on an epidemic of violence against women in India, where a rape is reported on average every 20 minutes. Media coverage of such crimes has intensified in the wake of the outcry over the Delhi attack.
Five men and a teenager have been detained over the attack and police sources on Tuesday said charges would likely be filed on Wednesday or Thursday.
Police are seeking the death penalty against four of the accused, one senior police source told Reuters.
They will also likely be charged with gang rape, abduction and destruction of evidence, the source said. The juvenile can not be executed under Indian law, although the victim's brother has called for all the accused to be hanged.
Anger at the brutality of the assault and the slow footed response from authorities spilled into the streets before Christmas, with police and protesters fighting running battles near the heart of government in Delhi.
The Indian Medical Association has questioned the decision to move the victim, who was suffering a massive blood infection and organ injuries, to Singapore, where she died.
On Tuesday police said they arrested a man who attempted to plant a low intensity explosive device near the house of one of the accused. The device was safely detonated, the force said.