The cremation took place during a private ceremony in New Delhi soon after the woman's body arrived in the capital on a special Air India flight from Singapore, where she died at a hospital Saturday after being sent for medical treatment.
The tragedy has forced India to confront the reality that sexually assaulted women are often blamed for the crime, forcing them to keep quiet and discouraging them from going to authorities for fear of exposing their families to ridicule. Police often refuse to accept complaints from rape victims, and the rare prosecutions that reach courts can drag on for years.
Security was tight, with no access to the public or media at the crematorium.
Prime Minister Manmohan Singh and Sonia Gandhi, head of the ruling Congress party, were at the airport to receive the body and meet family members of the victim who were on the flight.
Hours after the victim died early Saturday, Indian police charged six men who had been arrested in connection with the attack with murder, adding to accusations that they beat and gang-raped the woman on a New Delhi bus on Dec. 16.
New Delhi police spokesman Rajan Bhagat said the six suspects face the death penalty if convicted, in a case that has triggered protests across India and raised questions about lax attitudes by police toward sexual crimes.
After 10 days at a hospital in New Delhi, the victim, who has not been identified, was taken Thursday to Singapore's Mount Elizabeth hospital, which specializes in multi-organ transplants, but her condition worsened, with her vital signs deteriorating.
Following her death, thousands of Indians lit candles, held prayer meetings and marched through various cities and towns, including New Delhi, Mumbai, Bangalore and Kolkata, on Saturday night to express their grief and demand stronger protection for women and the death penalty for rape, which is now punishable by a maximum of life imprisonment.
But even as thousands mourned the rape victim's death and in a sign of how pervasive such crimes are, police in West Bengal state were investigating another suspected gang-rape and death.
In the latest case, the family of a woman said she and her husband were attacked by six men as they returned home after working at a brick factory.
They dragged the woman into a nearby farm after pouring acid into her husband's mouth, the family said.
The woman was found dead with multiple injuries, said police officer Bhaskar Mukherjee, adding he was waiting for an autopsy report.
No charges have been laid. Another police officer, Sugata Sen, said four men had been detained for questioning.
The alleged attack is similar to the Dec. 16 case, where the woman and a male friend, who also has not been identified, were on a bus after watching a film when they were attacked by six men who raped her. The men beat the couple and inserted an iron rod into the woman's body, resulting in severe organ damage. Both were then stripped and thrown off the bus, according to police.
Dozens of protesters tried to break through a police cordon Sunday and march to the parliament building in the Indian capital, but were pushed back. The protesters, belonging to the student wing of main opposition Bharatiya Janata Party, shouted anti-government slogans as they marched.
Hundreds of policemen have sealed off the high-security area, where the seat of India's government is located, in anticipation of more protests. The area is home to parliament, the president's palace, the prime minister's office and several ministries.
Gandhi assured the protesters in a statement that the rape victim's death "deepens our determination to battle the pervasive, the shameful social attitudes and mindset that allow men to rape and molest women and girls with such an impunity."
Attitudes by Indians toward rape are so entrenched that even politicians and opinion makers have often suggested that women should not go out at night or wear clothes that might be seen as provocative.
Meanwhile, a United Nations statement said U.N. Secretary-General Ban Ki-moon "offers his sincerest condolences" to the victim's family and "utterly condemns this brutal crime."
"Violence against women must never be accepted, never excused, never tolerated," the statement said. "Every girl and woman has the right to be respected, valued and protected."
Ban urged the Indian government to take steps to deter such crimes and bring perpetrators to justice, and to "strengthen critical services for rape victims," it said.
Image: An ambulance transporting the body of a gang-rape victim is seen outside her residence in New Delhi on December 30, 2012. The body of a gang-rape victim arrived back in New Delhi on December 30 after her death from sickening injuries in a Singapore hospital as India was engulfed by a mass outpouring of grief and anger. (AFP)