Markets across the country were all decked up where Muslim men and women were seen doing last minute shopping before the festival of sacrifice.
Eid-ul-Azha commemorates the willingness of Ibrahim to sacrifice his son as an act of obedience to Allah.
President Pranab Mukherjee, Vice President Hamid Ansari and Prime Minister Manmohan Singh greeted the people, saying it is an occasion to remind ourselves of the path of selfless sacrifice and forgiveness.
"May this festival spread peace and harmony and bring prosperity to all," Singh said in his message.
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The President hoped that the festival will knit the people of India "in a celebration of our composite culture".
"On the occasion of Eid-ul-Azha, I extend my greetings and good wishes to all fellow citizens and, in particular, to my Muslim brothers and sisters," Mukherjee said.
The spirit of sacrifice and service is the essence of the festival. It is an occasion to remind ourselves of the path of selfless sacrifice and forgiveness followed by Hazrat Ibrahim and to emulate the same, he said.
Ansari said the festival celebrates the treasured ideals of compassion, sharing and sacrifice.
"Let us observe this joyous occasion by spreading the message of peace, harmony and goodwill in our midst," he said.
Celebrating the festival, Muslims will wear new cloths and sacrifice sheep or goat. The meat is then distributed to family members, neighbours and the poor.