(CNN) -- An Indian woman whose gang-rape aboard a bus in New Delhi spawned mass protests has died, according to a doctor who was treating her at a Singapore hospital.
The woman, 23, "passed away peacefully" at 4:45 a.m. Saturday (3:45 p.m. ET Friday), with her family and Indian officials at her side, Dr. Kelvin Loh, chief executive officer at Mount Elizabeth Hospital, said in a statement.
The woman had been in "extremely critical condition" since being admitted Thursday to the Singapore hospital, and Loh had said Friday that she'd "taken a turn for the worse."
"She had suffered from severe organ failure following serious injuries to her body and brain," Loh said. "She was courageous in fighting for her life for so long against the odds, but the trauma to her body was too severe for her to overcome."
An Indian activist gets his head shaven in protest against the Dehli gang-rape in New Delhi on Friday, January 4. A gang of men is accused of repeatedly raping a 23-year-old student on a moving bus in New Delhi. Police formally charged the five suspects with rape, kidnapping and murder after the woman died.
Photos: India rape protest
Authorities haven't released the name of the rape victim, but Indian protesters are calling her Damini, which means "lightning" in Hindi. "Damini" also is a 1993 Bollywood film whose lead female character fights for a housemaid, a victim of sexual assault.
T.C.A. Raghavan, India's ambassador to Singapore, said the family wants its privacy protected. He said they are Hindu and from New Delhi.
"It's been a very trying and difficult time for them," he said of the late woman's family. "They are in the process of getting in touch with all their relatives and deciding the next steps."
Read more: India gang-rape victim in Singapore for treatment; new protests hit New Delhi
Attackers assaulted the woman and her male companion on a bus December 16, robbing them of their belongings before dumping them at the side of a road, police said. Six suspects are now under arrest, including the bus driver and a minor.
The male companion was eventually discharged from a hospital, but the female victim's condition deteriorated as she spent days in intensive care, battling for her life.
Police said last Saturday that she had recovered enough to give a statement to a magistrate from her hospital bed the night before. But on Sunday, she underwent another surgery to wash out infection in her abdomen, her doctors said.
The death spurred an outpouring of sadness in social media, as well as calls for action to ensure her rapists are punished and that Indian society changes so that more women aren't assaulted, harassed and otherwise mistreated because of their gender.
"'Damini' (is) just a name now," famed Bollywood actor Amitabh Bachchan wrote on Twitter. "Her body has passed away, but her soul shall ... forever stir our hearts !!!"
Prime Minister Manmohan Singh offered his "deepest condolences" early Saturday upon learning of the woman's death, and said "it is up to us all to ensure that her death will not have been in vain."
"We have already seen the emotions and energies this incident has generated," he said, referring to widespread protests calling for justice and reforms since the December 16 attack. "These are perfectly understandable reactions from a young India and an India that genuinely desires change.
"It would be a true homage to her memory if we are able to channel ... these emotions and energies into a constructive course of action."
Reported rape cases in India -- where a cultural stigma keeps many victims from reporting the crime -- have increased drastically over the past 40 years from 2,487 in 1971 to 24,206 in 2011, according to official figures. New Delhi alone had 572 rapes reported last year and more than 600 in 2012.
One such recent case involved a 17-year-old girl who claimed she'd been gang-raped during the Hindu festival of Diwali on November 13, though a formal case wasn't registered by police until 14 days later.
She committed suicide Wednesday by ingesting poison, according to Paramjit Singh Gill, the inspector-general of police in the Patiala district of Punjab, in northern India. In her suicide note, the teenager blamed her alleged rapists. Three suspects -- including a female accomplice -- have since been arrested, Gill said.
Seema Sirohi, of the Indian Council on Global Relations, said most women in Indian have stories of sexual harassment and abuse on public transportation, on the streets, and elsewhere. Regardless of how a woman dresses, "You are still open season for men."
"There are a lot of reasons why this happens, but the patriarchal system is one, a lack of policing is another, and general treatment of women is not equal to men, even though it may be so under the law," Sirohi said.
Before "Damini's" death, the prime minister called assuring women's safety his government's "highest concern." He said women's emergence in public "is accompanied by growing threats to their safety and security."
"Women and girls represent half the population, and our society has not been fair to this half," Singh said in a speech Thursday. "Their socio-economic status is improving, but gaps persist."
The Indian government announced plans Thursday to "name and shame" convicted rapists by posting their names, images and addresses on official websites, according to the Times of India.
And the Cabinet plans to set up a commission to look into rape cases and suggest measures to improve women's safety. This group has three months to submit its report to the government. Singh said his "government is examining, on priority basis, the penal provisions that exist for such crimes and measures to enhance the safety and security of women."
"I hope that the entire political class and civil society will set aside narrow sectional interests and agendas to help us all reach the end that we all desire -- making India a demonstrably better and safer place for women to live in," the prime minister said.
CNN's Greg Botelho, Harmeet Shah Singh and Hilary Whiteman contributed to this report.
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Indian lawyers shout during a protest at the entrance to Saket District Court in New Delhi on Thursday, January 3.
About 600 guitarists play John Lennon's "Imagine" in a tribute to the rape victim in Darjeeling on January 3.
Indian women take part in the Women's Dignity March in New Delhi on Wednesday, January 2. Several hundred people participated in the solidarity march organized by the government, which ended at Rajghat, the memorial for Mohandas Gandhi.
Delhi Chief Minister Sheila Dikshit, center, participates in a group prayer during the Women's Dignity March on January 2.
Indian demonstrators perform a prayer ritual in memory of a gang-rape victim in New Delhi on Monday, December 31. The family of the victim said they would not rest until her killers are hanged as they spoke of their own pain and trauma over a crime that has united the country in grief.
A Sri Lankan opposition United National Party activist places her signature on a banner in memory of the Indian gang-rape victim in Colombo on December 31.
Indian protesters hold candles during a rally in New Delhi on Sunday, December 30, following the cremation of the gang-rape victim.
Indian protesters walk with police officials during a rally in New Delhi on Sunday, December 30, following the cremation of a gang-rape victim in the Indian capital. The 23-year-old student died Saturday and was cremated at a private ceremony, hours after her body was flown home from Singapore. She had been gang-raped and severely beaten on December 16, triggering an outpouring of grief and anger across India.
Indian protesters sit by lit candles and hold placards in New Delhi on December 30 during a protest against the gang rape.
Indian residents pray during a gathering in New Delhi on December 30.
Protesters hold candles during a vigil in New Delhi on Saturday, December 29, after the death of a gang-rape victim. Authorities erected security barriers throughout New Delhi's key government district after two days of street battles following a woman's gang rape on a bus on December 16. Indian Prime Minister Manmohan Singh has appealed for calm and pledged safety for women and children.
Indian residents hold lighted candles during a rally in Amritsar on December 29.
Students in New Delhi on Thursday, December 27, protest a recent brutal gang rape in the city.
Demonstrators shout slogans and wave placards as they move toward India Gate in New Delhi on December 27.
Riot police keep watch along a sealed-off road near the India Gate monument on Monday, December 24, in New Delhi after weekend clashes between protesters and police.
Police fire tear gas on Sunday, December 23, during a protest calling for better safety for women following last week's rape. Thousands of protesters defied a ban on demonstrations in New Delhi on Sunday, venting their anger about the incident.
Police attempt to disperse protesters on December 23. For a second day, demonstrators were blasted with water cannons in the Indian capital. While some dispersed, others huddled tightly in a circle to brave high-pressure streams in the cold weather.
Demonstrators turn a car over on December 23.
Students chant anti-police slogans during a protest against the Indian government's reaction to recent rape incidents in India, on Saturday, December 22, in New Delhi, India. The demonstration was prompted by wide public outrage over what police said was the gang-rape and beating of a 23-year-old woman on a moving bus in the capital last Sunday.
Demonstrators react from tear gas fired by police on December 22. New Delhi alone reported 572 rapes last year and more than 600 in 2012.
Police arrest a demonstrator during a protest on December 22. Sunday's attack sparked furious protests across India, where official data show that rape cases have jumped almost 875% over the past 40 years -- from 2,487 in 1971 to 24,206 in 2011.
Police unleash water cannon and fire tear gas towards demonstrators on December 22.
Demonstrators react as police fire tear gas on December 22.
Indian demonstrators march towards India Gate during the protest on December 22.
Indian demonstrators carry an injured man from the scene on December 22.
Police spray water and fire tear gas towards demonstrators on December 22.
Demonstrators push against a police barricade on December 22.
Students chant anti-police slogans on December 22.
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