Additional Director General Munir Khan said there were localised incidents in various parts of Srinagar and other districts in the Valley, but these were contained and dealt with locally.
There have been no major injuries to anyone, he said at a press conference.
He added that there were a few pellet injuries in the Valley that have been treated.
"Our biggest endeavour is to ensure there is no civilian casualty," Khan told reporters.
"Restrictions imposed in Jammu have been completely removed and schools and other establishments there are functioning. Restrictions will continue in some places of Kashmir for sometime," he told reporters here.
Asked about the number of people detained, Khan said he would not talk about individuals.
"In a law and order situation like this, there are different kinds of detention... preventive detention to ensure the established miscreants do not vitiate the peaceful atmosphere... so you have to take preventive steps," he said.
The main focus of the administration and the police is now on Independence Day celebrations on Thursday, the officer said.
"All arrangements are in place to ensure peaceful celebrations throughout the state," he added.
Jammu and Kashmir Principal Secretary Rohit Kansal, who also addressed the media, said the overall situation in the state remained calm.
"Further relaxations in prohibitory orders have been given in a large number of areas, including in Srinagar, and these relaxations will continue to be given till this afternoon," he said.
On all other fronts -- civil supplies, national highways, airport, medical facilities -- the situation was normal, Kansal said.
"Local authorities, as before, are keeping a close watch on the situation and offering relaxations wherever the situation warrants it," he said.
Giving details of the situation in the Valley, Khan said curbs are in place in certain places. Restrictions, he added, are imposed after assessing the overall situation of that particular area.
"It is not like restrictions are imposed in a generalised manner. After assessing the situation of a particular area, restrictions are imposed... relaxation is also given after assessing the situation (of the area concerned)," the ADG said.
It is for the district administration -- the district magistrate and the district SP -- to assess the situation and take steps necessary to maintain peace, and law and order.
Asked about propaganda from Pakistan, Khan said the neighbouring country unleashes such propaganda whenever there is any major law and order situation in the state and all measures are being taken to thwart its attempts.
"You will see the results very soon," he said.
Responding to a query about some Twitter accounts circulating fake news and spreading misinformation, the officer said they have been identified and action initiated against them.
His message to the people of Kashmir, he said, was to celebrate August 15 with fervour.
The clampdown came into force on August 5 when the Centre stripped Jammu and Kashmir of its special status and bifurcated it into the union territories of Jammu and Kashmir, and Ladakh.
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