Shops and private and public transport services remained closed in Srinagar and some other towns in Kashmir following restrictions imposed by authorities.
"These are preventive measures taken to maintain law and order in the city and some other places in the valley," said a senior police officer.
Separatist groups have called for a three-day protest shutdown till Tuesday to commemorate the death anniversary of Guru and Bhat, who were hanged in Tihar Jail in New Delhi on February 9, 2013, and February 11, 1984, respectively. They were subsequently buried in the jail compound.
"Our struggle for return of mortal remains will continue," said JKLF chief Yasin Malik.
All separatist leaders, including Malik, Shabir Ahmad Shah and Muhammad Nayeem Khan have been taken into preventive custody by the police, while hardline separatist leader Syed Ali Geelani has been placed under house arrest.
Sporadic incidents of protesters throwing stones at the security forces were witnessed on Sunday at a few places in Ganderbal, Baramulla and Bandipora districts.
Police said the security forces exercised restraint while bringing the situation under control and nobody was injured in the clashes.
Meanwhile, Kashmir University has postponed all its exams scheduled for Monday and Tuesday.
(With inputs from IANS)