"Two persons have died in an incident of violence in Kulgam district yesterday and have been identified as Feroze Ahmad Mir (22) and Khursheed Ahmad Mir (38)," a police official said.
With this, the death toll in the violence has gone up to 23, including a policeman.
Normal life has been paralysed due to curfew-like restrictions and separatists-sponsored strike since Saturday.
Security forces tried to chase away the mob but the attackers were regrouping and intermittently hurling stones, he said.
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Three persons were injured yesterday when security forces opened fire to disperse a mob which was pelting stones at the air force base.
One person was injured in police action against protesters in Ganderbal district.
Stone pelting incidents were reported from Sopore, Handwara, Bandipora and Baramulla in north Kashmir, the official said.
Mobile telephony has been suspended in four districts of south Kashmir since Friday evening as violent protests erupted following killing of Wani in an encounter with security forces. Mobile internet services continued to remain suspended.
Strict restrictions on movement of people continued to be in place in many parts of the Valley including parts of Srinagar city, where the first death in the clashes occurred last evening.
Authorities have strengthened the presence of security forces in vulnerable areas of the city and elsewhere in the Valley to contain the protests, police said.
Shops, private offices, business establishments and petrol pumps were shut, while government offices and banks witnessed thin attendance, officials said.
Public transport was completely off the roads while private cars and auto-rickshaws were seen plying at few places in the areas where there were no restrictions, they said.
Educational institutions in the Valley were closed on account of the ongoing summer vacations, while Central University of Kashmir (CUK), Islamic University of Science and Technology (IUST) and Jammu and Kashmir Board of School Education (JKBOSE) have postponed the examinations due to the prevailing situation.