Rao died Thursday of heart failure following a long illness. He was 83.
Current Prime Minister Manmohan Singh was present at the funeral. He declared a seven-day period of national mourning.
However, Sonia Gandhi, president of Rao's Congress party, was not in attendance.
Rao served as prime minister between 1991 and 1996. He is credited with a series of economic reforms.
Selena Gomez drops F-bomb, walks off stage during Jingle Ball performance
'SNL': 'Anchorman 2' cast, One Direction sing 'Afternoon Delight' [VIDEO]