There was a heavy police presence at the funeral amid on-going protests
A young Indian woman who died after being gang-raped on a bus has been cremated in the capital, Delhi.
The ceremony came hours after a plane chartered by the Indian government brought her body back to the city.
The 23-year-old medical student died in a Singapore hospital where she was being treated for severe injuries.
The attack sparked two weeks of protests about gender attitudes in India, and calls for changes to laws on rape and violence against women.
Indian Prime Minister Manmohan Singh and the head of India's governing Congress party Sonia Gandhi were at the airport when the plane landed at about 04:15 (22:45 GMT).
A convoy carrying a gold-coloured coffin and the victim's parents then drove towards the Janakpuri district of Delhi where she had been living.
The private funeral was held amid tight security.
The BBC's Andrew North in Delhi says the government has been heavily criticised for its response to the attack and remains anxious about a backlash, with police still cordoning off the heart of the capital to prevent demonstrations.
Mrs Gandhi has promised to fight what she called India's shameful social mindsets that lie behind such crimes.
Six men arrested for the 16 December rape have been charged with murder. If convicted, they face the death penalty.
'Open our eyes'
On Saturday evening, candlelit vigils were held across India to mourn the woman and express anger and sorrow at her death.
Large areas of Delhi were sealed off and hundreds of armed police and riot troops deployed as news of the victim's death spread.
Protests continued in Delhi on Sunday, with a peaceful demonstration where people painted slogans and tributes on a large white canvas.
"This incident should open our eyes to the fact that we need to raise our children right, we need to raise the people right," said protester and social worker Murphy John.
He said he did not agree with calls for the death penalty for convicted rapists, fearing it would encourage murder so victims could not report crimes.
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.
Indian PM Mr 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.
Friends told the AFP news agency the couple were in a relationship and had been planning to marry in the next few weeks.
"They had made all the wedding preparations and had planned a wedding party in Delhi," said her neighbour, Meera Rai.
According to the reports, the couple were attacked after the man objected to another group of men taunting her.
Police said the woman was raped for nearly an hour. 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.
According to official figures, a woman is raped in Delhi every 14 hours, while women across the country say they are frequently subjected to sexual intimidation and violence.
Officials have since announced a series of measures intended to make the city 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.
But many of the protesters say that women are viewed as secondary citizens, and that a fundamental change in culture and attitudes, backed up by law, is needed to protect them.
UN Secretary Ban Ki-moon offered his condolences to the woman's family, saying in a statement that he "utterly condemns this brutal crime".
"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."