However, Muslims in Haryana's Khandwali village wore black bands on their arms as a protest against the lynching of a local youth recently in Ballabhgarh on suspicion of carrying beef.
Across the length and breadth of the country, Muslims thronged mosques, shrines and eidgahs since early morning to offer special prayers on Eid-ul-Fitr, which marks the end of the fasting month of Ramzan.
Along with the special prayers, feasts were held by the Muslims to celebrate the occasion in which members from other communities also participated.
President Pranab Mukherjee, Vice President Hamid Ansari, Prime Minister Narendra Modi and other political leaders extended their greetings, wishing that the festival ushers in peace and harmony in the country.
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In Kashmir, which has been witnessing increased violence for some time, people celebrated the festival with immense fervour and devotion.
Muslims from all walks of life offered prayers at Eidgahs (prayer ground) and mosques and visited relatives and friends to greet them on the occasion.
Hazratbal shrine on the outskirts of Srinagar saw more than 50,000 faithfuls offering their prayers while the Eidgah in old city had the second largest gathering of 40,000 devotees.
Barring a few incidents of stone-pelting after the prayers, the situationin the Valley remained peaceful.
Clashes between protestors and law enforcing agencies were reported from Sopore,Anantnag,Rajpora,Shopian towns and Safakadal area of the city.
There were no reports of anyone getting hurt in these clashes.
The authorities had placed top separatist leaders, including Syed AliGeelani and Mirwaiz Umar Farooq, under housearrest, fearing that their presence at large Eid gatherings could sparkviolence, the officials said.
Home Minister Rajnath Singh, in a special video message for the people of Kashmir, expressed confidence that the festival would help bring peace and happiness to the Valley.
"I am fully confident that this festival of goodness and humanity will help in bringing peace, understanding, brotherhood and happiness in Kashmir Valley and pave the way for a new dawn there," he said.
In the national capital, Muslims visited mosques and eidgahs, including the historic Jama Masjid, Fathepuri Masjid and Hazrat Nizamuddin, to offer prayers.
In Haryana's Khandwali village, whose resident Junaid (17) was killed on June 22, Muslims wore black armbands during the special morning prayers.
"We could not have celebrated Eid with the usual sense of joy considering how Junaid was killed. So we decided to mark our protest by wearing black bands around our arms," Shakeel, a resident of Khandawli in Ballabgarh near Delhi, said.
He claimed Muslims of neighbouring villages were also protesting by wearing black armbands during prayers.
In West Bengal, the celebrations were low-key in Darjeeling hill areas which have been witnessing protests and bandhs over the demand for separate Gokhaland state.
Muslims in other eastern and Northeastern states like Bihar, Nagaland, Meghalaya, Mizoram also celebrated the festival.
But for the exiled Rohingya Muslims in Delhi, it was just any other day.
There are nearly 900 Rohingya refugees in camps in Shaheen Bagh, Madanpur Khadar, Okhla and Vikaspuri. While some work as ragpickers and sweepers, others find small time jobs in NGOs and private offices. They fast but do not feast.