* India PM says emotions should be channelled into action
* Attack has triggered outrage, protests
* New Delhi locked down but protesters still gather peacefully
* Suspects charged with murder (Adds departure of plane carrying her body, estimated time of arrival in India, paragraph 16)
By Ross Colvin and Kevin Lim
NEW DELHI/SINGAPORE, Dec 29 (Reuters) - A woman whose gang rape provoked protests and rare national debate about violence against women in India died from her injuries on Saturday, prompting promises of action from a government that has struggled to respond to public outrage.
The unidentified 23-year-old medical student suffered a brain injury and massive internal damage in the attack on Dec. 16 and died in hospital in Singapore where she had been taken for treatment.
Protesters rallied peacefully in the capital New Delhi and other cities across India to keep the pressure on Prime Minister Manmohan Singh's government to get tougher on crimes against women. That was in contrast to the pitched battles protesters fought with police last weekend.
The six suspects held in connection with the attack on the student on a New Delhi bus were charged with murder following her death, police said. The maximum penalty for murder is death.
Authorities, worried about the reaction to the news of her death, deployed thousands of policemen, closed 10 metro stations and banned vehicles from some main roads in the heart of New Delhi, where demonstrators have converged since the attack to demand improved women's rights.
Despite efforts to cordon off the city centre, more than 1,000 people gathered at two locations. Some protesters shouted for justice, others for the death penalty for the rapists.
Most sex crimes in India go unreported, many offenders go unpunished, and the wheels of justice turn slowly, according to social activists who say that successive governments have done little to ensure the safety of women.
Political leaders vowed steps to correct "shameful social attitudes" towards women in the world's biggest democracy.
"The need of the hour is a dispassionate debate and inquiry into the critical changes that are required in societal attitudes," the prime minister said in a statement.
"I hope that the entire political class and civil society will set aside narrow sectional interests and agenda 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 woman, beaten, raped and thrown out of a moving bus, had been flown to Singapore in a critical condition by the Indian government on Thursday.
She and her male friend were returning home from the cinema, media reports say, when six men on the bus beat them with metal rods and repeatedly raped the woman. Media said a rod was used in the rape, causing internal injuries. The friend survived.
"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," Kelvin Loh, chief executive officer of the Mount Elizabeth Hospital in Singapore said in a statement announcing her death from multiple organ failure.
The Indian government has chartered an aircraft to fly her body back to India, along with family members, T.C.A. Raghavan, the Indian high commissioner to Singapore, told reporters.
The body was taken from the hospital to a Hindu undertaker in Singapore and hours later, lying in a gold and yellow coffin selected by Indian diploamts, the body was driven in a hearse to the airport.
The plane took off from Singapore at 1630 GMT and was expected to reach New Delhi around 3 a.m. local time on Sunday (2130 GMT Saturday), the NDTV channel reported on its website citing the High Commissioner.
Hundreds of protesters took to the streets in the northern Indian city of Lucknow. In Hyderabad, in southern India, a group of women marched to demand severe punishment for the rapists. Protests were also held in the cities of Chennai, Kolkata and Mumbai.
"For some reason, and I don't really know why, she got through to us," well-known columnist Nilanjana Roy wrote in a blog on Saturday.
"Our words shrivelled in the face of what she'd been subjected to by the six men travelling on that bus, who spent an hour torturing and raping her, savagely beating up her male friend."
Sonia Gandhi, the powerful leader of the ruling Congress party, directly addressed the protesters in a rare broadcast on state television, saying that as a mother and a woman she understood their grievances.
"Your voice has been heard," Gandhi said. "It deepens our determination to battle the pervasive and the shameful social attitudes that allow men to rape and molest women with such impunity."
The attack has put gender issues centre stage in Indian politics. Issues such as rape, dowry-related deaths and female infanticide have rarely entered mainstream political discourse.
Analysts say the death of the woman dubbed "Amanat", an Urdu word meaning "treasure," by some Indian media could change that, although it is too early to say whether the protesters calling for government action to better safeguard women can sustain their momentum through to national elections due in 2014.
The outcry over the attack caught the government off-guard and it was slow to react. It took a week for Singh to make a statement on the attack, infuriating many protesters who saw it as a sign of a government insensitive to the plight of women.
The prime minister, an 80-year-old technocrat who speaks in a low monotone, has struggled to channel the popular outrage in his public statements and convince critics that his eight-year-old government will take steps to improve the safety of women.
"The Congress managers were ham-handed in their handling of the situation that arose after the brutal assault on the girl. The crowd management was poor," a lawmaker from Singh's ruling Congress party said on condition of anonymity.
Commentators and sociologists say the rape has tapped into a deep well of frustration many Indians feel over what they see as weak governance and poor leadership on social issues.
A global poll by the Thomson Reuters Foundation in June found that India was the worst place to be a woman because of high rates of infanticide, child marriage and slavery.
New Delhi has the highest number of sex crimes among India's major cities, with a rape reported on average every 18 hours, according to police figures. Government data show the number of reported rape cases in the country rose by nearly 17 percent between 2007 and 2011. (Additional reporting by Devidutta Tripathy, Satarupa Bhattacharjya, Diksha Madhok, Shashank Chouhan and Suchitra Mohanty in Delhi, Sharat Pradhan in Lucknow, Sujoy Dhar in Kolkata, Anupama Chandrasekaran in Chennai, Eveline Danubrata, Saeed Azhar, Edgar Su and Sanjeev Miglani in Singapore; Editing by Mark Bendeich, Robert Birsel and Alison Williams)