An Indian woman who died from injuries sustained after being gang-raped on a bus in New Delhi has been cremated.

An outpouring of anger and grief was displayed by millions across the country demanding greater protection for women from sexual violence.

The young woman's body was cremated in a private ceremony in New Delhi soon after it arrived in the capital on a special Air India flight from Singapore.

The woman died at a hospital yesterday after being sent for medical treatment.

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 had also arrived on the flight.

Hours after the victim died early yesterday, Indian police charged six men, who had been arrested in connection with the attack, with murder.

These charges were added to accusations that they beat and gang-raped the woman on a New Delhi bus on 16 December. 

New Delhi police spokesman Rajan Bhagat said the six suspects face the death penalty if convicted.

The case has triggered protests across India and raised questions about lax attitudes by police toward sexual crimes.

A statement issued by United Nations spokesman Martin Nesirky said UN Secretary-General Ban Ki-moon "offers his sincerest condolences" to the victim's family and "utterly condemns this brutal crime".

Mr Ban said: "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."

He urged the Indian government to take steps to deter such crimes and bring perpetrators to justice, and to "strengthen critical services for rape victims," the statement said.

After ten days at a hospital in New Delhi, the victim, who has not been identified, was taken last Thursday to Singapore's Mount Elizabeth Hospital.

This hospital specialises in multi-organ transplants.

She arrived there in an extremely critical condition, and then took a turn for the worse, with her vital signs deteriorating.

She died with her family and officials of the Indian Embassy by her side.

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 last night.

People marched 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.

Women face daily harassment across India, ranging from catcalls on the streets, groping and touching in public transport to rape.

The tragedy has forced India to confront the reality that sexually assaulted women are often blamed for the crime.

Victims often feel forced to keep quiet and discouraged from reporting it to authorities for fear of exposing their families to ridicule.

Police often refuse to accept complaints from those who are courageous enough to report the rapes, and the rare prosecutions that reach courts drag on for years.

Prime Minister Singh said yesterday that he was aware of the emotions the attack has stirred.

He added that it was up to all Indians to ensure that the young woman's death will not have been in vain.