The Hurriyat Conference, of which Malik's party is a member, has called a two-day shutdown against the killing and called for a "march to Tral" on May 30.
Valley police chief Muneer Khan said the civilian died in cross firing between the holed up militants and the security forces.
Restrictions have been imposed in Khanyar, Nowhatta, Safakadal, M R Gunj, Rainawari, Kralkhud and Maisuma police station areas of the city till further orders as a precautionary measure in view of the prevailing law and order situation.
Bhat was buried past midnight in his ancestral graveyard in Rutsana village, as hundreds converged - arriving from different areas, amid massive security. On being challenged, the militants opened fire, and in the encounter that ensued, six infiltrators were felled, the army said.
"We will welcome them (Kashmiri Pandits) warmly and there is always place for them in our hearts". The initiative has begun.
Even as the curfew remains in place, Home Minister Rajnath Singh has asserted that the Modi government had found a permanent solution to Kashmir.
Similarly, curfew-like restrictions will continue in the south Kashmir districts of Shopian, Pulwama, Kulgam and Anantnag on Tuesday, authorities said.
All educational institutions have been shut in the valley and exams scheduled for Monday in the university have been postponed.
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Reports of severe restrictions also poured in from old town Baramulla, main town Sopore.
In all the restrictions were in place in four out of 10 districts in the valley. They said public transport was off the roads, but private cars, cabs and auto-rickshaws were seen plying.
The Tral operation is a coordinated effort of the Rashtriya Rifles (RR), the JKP, Special Operation Group (SOG) and the Central Reserve Police Force (CRPF).
Indian authorities have gagged the region once again, partially cutting telephone services and snapping internet mobile services, just hours after a month-long ban on 22 social media sites had ended.
Anti-India sentiment runs deep in the Kashmir valley, where most people favour independence from India.
Rebel groups have largely been suppressed by Indian forces in recent years.
After the death of the two militants on Saturday morning, pro-independent protests erupted across the region with unarmed civilians clashing with Indian forces. Tens of thousands of people, mostly civilians, have been killed in the almost three decade-old conflict.
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