NEW DELHI (AP) -- A young woman who died after being gang-raped and beaten on a bus in India's capital was cremated Sunday amid an outpouring of anger and grief by millions across the country demanding greater protection for women from sexual violence.

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.