Restrictions on the movement of people were imposed in Khanyar, Safakadal, Maharaj Gunj, Nowhatta, Rainawari and Maisuma police station areas as a precautionary measure to maintain law and order, a police official said.
He said there were apprehensions of law and order problems during the Hurriyat Conference rally at Eidgah on old city area.
The official said the situation across the Valley was peaceful so far with no untoward incident reported from anywhere.
Criticising the move, a Hurriyat Spokesman said, "When Kashmiris were peacefully organizing Hafta Shahadat to remember (Mirwaiz's father) Mirwaiz Mohammad Farooq, (Hurriyat leader) Abdul Gani Lone...Placing him under house arrest was like rubbing salt on the wounds of Kashmiris."
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Farooq was shot dead by militants on May 21, 1990, and Lone fell to the bullets of ultras during a commemoration rally for the former on the same day in 2002.
Schools and business establishments were closed in most parts of the Valley but some schools in the interiors of the city were functional.
Public transport remained off the roads but private vehicles could be seen plying the roads in the city and other parts of the Valley, officials said.