Groups of youth indulged in stone-pelting on police and paramilitary personnel outside Jamia Masjid in Srinagar after the Friday prayers, the officials said.
They said police and paramilitary personnel used teargas shells and batons to disperse the protesters.
The separatist camp comprising chairmen of both factions of Hurriyat Conference, Syed Ali Geelani and Mirwaiz Umar Farooq, and JKLF chief Mohammad Yasin Malik had called for protests after Friday prayers against what it called "state terrorism".
In Bomai area of Sopore, students of government higher secondary school boycotted their classes in the morning and staged a protest against the arrest of students during the ongoing agitation.
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Clashes ensued, during which police was targeted in the main town after Friday prayers, the officials said.
They said police fired dozens of teargas shells and used batons to disperse the stone-pelting protesters to restore order.
Barring these few incidents of stone-pelting, the officials said overall situation in the valley remained by and large peaceful.
The students are agitating over the alleged highhandedness of police and are demanding action against the erring personnel for roughing up students.
A number of students were arrested during clashes in Srinagar and elsewhere in the valley.