Prohibitory orders banning large gatherings was re-imposed in Srinagar on Sunday, a day after the government said sporadic clashes took place in the city after the restrictions were relaxed Saturday.
Sources said police vehicles were seen making announcements on loudspeakers asking people to return to their homes, and shopkeepers have been told to shut their shops.
On Saturday, a Home Ministry spokesperson said there have been "stray protests" in Srinagar and Baramulla, none of which involved a crowd of more than 20 people.
Asked about Congress leader Rahul Gandhi's claims that huge protests have taken place in the state, police chief Dilbagh Singh said there has been no untoward incident "barring minor stone-pelting which was dealt with on the spot".
The Home Ministry also dismissed media reports about a protest by some 10,000 people in Kashmir valley as "fabricated and incorrect".
The situation in Jammu and Kashmir is peaceful and no violence has been reported from anywhere in the state, the state police had tweeted.
In a statement, the government said senior police officers and Chief Secretary BVR Subrahmanyam have asked people not to believe in rumours about alleged incidents of firing in Kashmir valley.
On Saturday, Srinagar and other towns saw good traffic for Eid shopping, it said.
Around 400 politicians including former chief ministers Omar Abdullah and Mehbooba Mufti have been under arrest since last week.
On Monday last, the BJP-led central government scrapped the special status accorded to Jammu and Kashmir through a presidential order and declared plans to bifurcate the state into two Union Territories. The bill cleared parliament and was signed by the President over the next few days.
Omar Abdullah's National Conference has appealed in the Supreme Court against the government's decision. In its petition - filed by party MPs Akbar Lone and Hasnain Masoodi - the party claimed the centre's move was "illegal".
National Security Advisor Ajit Doval, who has been camping in Jammu and Kashmir amid the lockdown, was seen in a video on Saturday talking with locals.