Curfew was imposed in Srinagar and a few other towns on Saturday, a day after security forces shot dead a man in Bijbehara. The separatists have called for a shutdown across the Kashmir Valley.
Curfew has been imposed in nine police station areas of Srinagar besides Anantnag and Bijbehera towns while restrictions are in place in Sopore, Baramulla, Handwara and Kupwara towns, a police officer said in Srinagar.
"Following information that miscreants and anti-social elements intend to disrupt peace and prompt the youths to violence, preventive measures have been taken to protect civilian life and property," he said.
The death toll in the ongoing unrest in the valley that started June 11 has risen to 62.
Nazir Ahmad, 28, was killed in firing by security forces on Friday in south Kashmir's Bijbehara town when a mob surrounded a police station and tried to set it ablaze using petrol bombs.
Another teenager, Mudasir Nazir, 18, was killed in firing by the Central Reserve Police Force (CRPF) in Sopore town when a mob attacked a CRPF team withdrawing after the day's duties there.
Residents of Sopore allege the CRPF troopers fired without provocation.
Police have registered a first information report (FIR) to investigate the killing and bring the guilty to book.
The separatist Hurriyat group headed by Syed Ali Geelani has asked people to observe a shutdown across the Valley Saturday as part of his group's "Quit Kashmir" campaign.
Shops, educational institutions, banks, post offices and businesses were closed because of curfew and restrictions in parts of the city.
And in areas where there were no restrictions, life was paralysed due to the separatist-sponsored shutdown.
Newspaper owners here have alleged that the distribution of their newspapers has been halted by police in both northern and southern parts of Jammu and Kashmir.
"Copies of newspapers are being seized by police before these can reach our distributors in north and south Kashmir districts," a newspaper editor here said.