The mortal remains were flown to the capital in a Special Aircraft of Air India and after landing at IGI airport, the plane was taken to its technical area where Prime Minister Manmohan Singh and Congress chief Sonia Gandhi were present to receive the body.
Both Singh and Gandhi spoke to the family members and consoled them.
The body was then taken to Mahavir Enclave residence where the girl lived and religious rituals were performed before taking it to the crematorium at Dwarka Sector 24 amid heavy deployment of Delhi Police and RAF personnel.
The cremation took place under a dense cover of fog.
Minister of state for Home Affairs R P N Singh, West Delhi MP Mahabal Mishra, Delhi BJP chief Vijender Gupta were also present at the cremation.
Media was not allowed in the crematorium.
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A Special aircraft of Air India carrying the mortal remains of the victim, who died in Mount Elizebeth hospital yesterday morning, landed at IGI airport here at around 3.30 am.
The girl, a physiotherapy student, was gangraped and brutally assaulted allegedly by six men in a moving bus in south Delhi on December 16 night. She died yesterday morning.
While undergoing treatment at Safdarjung hospital, she was shifted to the Singapore hospital for further treatment.
The aircraft AIC-380A took off from Singapore at around 12:30 AM local time (10:00 PM IST Saturday), Indian High Commission officials said.
On the chartered plane, sent by the Indian government, were her family members who have been in Singapore since the girl was brought to the hospital here in an extremely critical condition.
The victim, who underwent three surgeries, had damaged internal organs in the assault. She also suffered a cardiac arrest and brain injury.
Police have slapped murder charges, which has death penalty in rarest of rare cases, against the six accused and will file the chargesheet against them on January three.
Investigators said they will seek the harshest punishment for the culprits.