Thousands of people gathered in the Indian capital to express their grief and demand justice for the 23-year-old victim, who died earlier on Saturday.
Six men arrested in connection with the December 16 attack have now been charged with murder.
The victim’s body is being flown back home from Singapore, where she had been taken for specialist treatment.
The rape triggered violent public protests over attitudes towards women in India.
Large areas of Delhi were sealed off and hundreds of armed police and riot troops deployed as news of the victim’s death spread.
During Saturday, large crowds people gathered at sites where public gatherings were allowed.
These included the city’s Jantar Mantar observatory, where people lit candles in the woman’s memory.
“We are aware that this is not the first case, nor will it be the last case of gang-rape in India, but it is clear that we will not tolerate sex crimes anymore,” Rana, a lawyer, told the AFP news agency.
The victim’s coffin, draped in a white flag, was taken to Singapore’s Changi airport to be flown home, accompanied by her parents who were at her bedside when she died.
Over the past two weeks, the unnamed woman has became a symbol of the wider issue of how women are treated in India.
The Mount Elizabeth hospital in Singapore said the woman “passed away peacefully” early on Saturday.
Hospital chief executive Kelvin Loh said she had suffered severe organ failure following serious injuries to her body and brain.
India’s Home Affairs minister, Ratanjit Pratap Narain Singh, said he was “heartbroken” by her death.
“I can only assure the family that the government will take whatever steps are needed to ensure that her killers get the harshest punishment in the quickest of time,” he said.
Indian Prime Minister Manmohan Singh said he was “very saddened” by the woman’s death, and that the angry public reaction was “perfectly understandable”.
He called on politicians and the public to set aside “narrow sectional interest” and work together to make India “a demonstrably better and safer place for women to live in”.
The woman – a medical student whose identity has not been released – and her friend had been to see a film when they boarded the bus in the Munirka area of Delhi, intending to travel to Dwarka in the south-west of the city.
Police said she was raped for nearly an hour, and both she and her companion were beaten with iron bars, then thrown out of the moving bus into the street.
The assault sparked angry protests about the general conditions for women in India, and about what is seen as an inadequate police response to rape allegations.
Officials have since announced a series of measures intended to make Delhi safer for women.
These include more police night patrols, checks on bus drivers and their assistants, and the banning of buses with tinted windows or curtains.
The government has also said that it will post the photos, names and addresses of convicted rapists on official websites to shame them.
It has set up two committees – one looking into speeding up trials of cases involving sexual assaults on women, and the other to examine the lapses that might have led to the incident in Delhi.
But the protesters say the government’s pledge to seek life sentences for the attackers is not enough – many are calling for the death penalty.
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