raped and tortured in a moving bus in Delhi Dec 16 and left to die by a roadside.
But the family was also moved by a large number of messages of support they had received from everywhere, Raghavan told the media.
"They hope that the death of their child will lead to a better future for women in Delhi and India," he quoted them as saying.
Raghavan, said the woman's family was "shattered".
"The scale of her injuries (was) very great," Raghavan told the media.
"It was very trying for the family. The girl of course was unconscious... I must say they (the family) bore the entire process with a great deal of fortitude and a great deal of courage."
He said arrangements were on to take the body to India in line with the family's wishes. He said her body will be flown Saturday afternoon. TV cameras showed her body being wheeled out of the hospital before daybreak.
The gangrape victim was shifted out of Delhi's Safdarjung Hospital to Singapore Thursday in a desperate bid to save ber life after she suffered multi-organ failure.
President Pranab Mukherjee and Prime Minister Manmohan Singh condoled her death and vowed to do everything possible to make India a better place for women.
The victim, a physiotherapist intern in Delhi and who waged a courageous battle to live, "died peacefully at 4.45am" with her distraught family and Indian diplomats by her side, Singapore's Mount Elizabeth Hospital official Kelvin Loh said.
The government had said it would pay all her medical bills in Singapore.
The 23-year-old woman, whose name was never disclosed as is the accepted custom for rape victims, suffered multiple-organ failure after she was raped by six males, including a suspected juvenile, in a moving bus in Delhi for some 40 minutes Dec 16 night and dumped her by a roadside after being assaulted and brutalised with an iron rod.
Her male friend was also badly beaten up and thrown out of the bus. All six accuse have been arrested and are in Delhi's Tihar Central Jail.
Authorities in India shifted the woman, who had been on ventilator support since her rape, to Singapore Thursday in a last ditch attempt to save her life.
President Mukherjee called the victim "a true hero".
He said: "I am deeply distressed by the unfortunate demise of the girl. She was a brave and courageous girl who fought till the very last minute for her dignity and her life. She is a true hero and symbolizes the best in Indian youth and women."
"At the same time, let us resolve that this death will not be in vain, We will do everything possible to make sure that such an incident never happens again," he added.
Expressing his deepest condolences, Manmohan Singh said it was up to "us all to ensure that her death will not have been in vain" and India becomes "a demonstrably better and safer place for women to live in."
He said he joined the nation "in conveying to her family and friends" his deepest condolences at this terrible loss.
"I want to tell them and the nation that while she may have lost her battle for life, it is up to us all to ensure that her death will not have been in vain.
It would be a true homage to her memory, "if we are able to channelize these emotions and energies into a constructive course of action", he said.
"(The) government is examining, on priority basis, the penal provisions that exist for such crimes and measures to enhance the safety and security of women," he said in his statement.
The horrific gang-rape triggered angry demonstrations across India against growing sexual crimes against women. A policeman died in one such protest in the Indian capital.
The government also said that it would take urgent steps to crack down on crime against women and fast-track the prosecution of the accused, who now face possible death penalty.