Eid prayers were not allowed in most of the mosques in Srinagar where curfew-like curbs were re-imposed on Sunday amid fear of violence.
According to photos shared by the government, Eid prayers were held in smaller mosques.
People from different walks of lives peacefully celebrated the occasion. Residents did not face any kind of inconvenience while moving towards the mosques.
They offered namaz and were also seen greeting on duty police personnel.
"Eid prayers concluded peacefully in various parts of the valley. No untoward incident reported so far," the official Twitter handle of the Jammu and Kashmir Police posted on Monday morning.
Sharing a photo of people distributing sweets after offering namaz, Union Home Ministry spokesperson Vasudha Gupta tweeted: "Eid prayers offered peacefully in all local mosques of Anantnag, Baramulla, Budgam, Bandipore, without any untoward incident. Jamia Masjid old town Baramulla witnessed approx 10,000 people offering prayers.
"People come out in good numbers to pray on Eid in Jammu and Kashmir prayers concluded at prominent mosques in Srinagar and Shopian. Over 4,500 offer prayers at Eidgah Jammu."
Amid the celebrations, government vehicles carrying police and security personnel were seen running on almost all the deserted roads and streets which are generally crowded on this occasion.
In an attempt to maintain friendly atmosphere on the occasion, the Central Reserve Police Force (CRPF), which is deployed in Jammu and Kashmir for internal security, said it distributed sweets at Eidgah.
"As sweets and smiles are directly related to festivals, CRPF Jammu distribute both at Eidgah Jammu on this Eid-al-Adha. Eid Mubarak to you all," CRPF DIG M. Dinakaran tweeted.
On Sunday, a meeting was held between clerics and the Kashmir Divisional Commissioner Baseer Khan, Inspector General of Police (Kashmir) Swayam Prakash Pani and Srinagar District Magistrate Shahid Choudhary to ensure a peaceful and smooth celebration of Eid.
Choudhary, who visited some of the mosques and grounds where prayers was offered, said he was trying to reduce inconvenience and ease facilities.
He also said that more than 250 ATMs have been made functional in Srinagar and bank branches were also open.
Baseer Khan said the administration was doing everything to ensure a peaceful Eid.
The Jammu and Kashmir administration had eased the prohibitory orders in Kashmir Valley for the past few days for the people to make purchases for Eid.
In the Valley, people thronged the market places during the six hours of relaxation provided for purchases before Eid-al-Adha also known as Bakrid.
People in Srinagar had come out in large numbers to shop for Eid on Sunday before the restrictions were back.
"People are coming out and shopping for Eid. A large number of people came out today. Wherever there were restrictions, they were relaxed. We're trying to facilitate people who want to travel to Srinagar to meet their dear ones," said Rohit Kansal, Principal Secretary, Planning Commission, on Sunday.
Later in the day, sources said police vehicles were seen making announcements on loudspeakers asking people to return to their homes, and shopkeepers were told to shut down.
Thousands of security personnel remain in the Kashmir Valley and phone and internet services have still not been restored.
In his speech to the nation on August 9 post the revocation of Article 370, Prime Minister Narendra Modi had assured that the people of the state would not face any trouble in celebrating Eid and that the situation in the valley will return to normal gradually.
Jammu and Kashmir has been under lockdown since the government on August 5 abrogated Article 370, and has divided the state into two Union Territories.
( With inputs from IANS )