On Sunday, five militants were killed when Indian forces ambushed the house they were in for the night.
Professor Bhat went missing from Kashmir University last Friday, which upset students, who protested over his "mysterious disappearance".
"They way they (government forces) are killing our next generation, we can not be mute spectators to it".
A police spokesman said the circumstances surrounding the death of civilians was being investigated.
The Jammu and Kashmir government has imposed restrictions in parts of the Kashmir valley ahead of a sit-in protest called by separatists.
Muslim-majority Kashmir has always been captured in a tug of war involving India and Pakistan, sparking violent separatist moves inside the region.
Inspector General of Police, Kashmir, S P Pani said repeated attempts were made to persuade the assistent professor to surrender. He was killed in an encounter and he was one among the five who got killed.
Chennai tourist injured in stone-pelting dies in Kashmir
On April 30, seven tourists were injured when stone-throwers targeted vehicles in south Kashmir's Anantnag district. Thirumani was taken to SKIMS hospital at Soura, where he succumbed to the injuries later, the official added.
Some Kashmiri groups in Jammu and Kashmir have been fighting against Indian rule for independence, or for unification with neighboring Pakistan.
During the gun-battle, the police made several appeals to the militants to surrender and also made their family members talk to them.
Reports from South Kashmir's Shopian said that district wore a deserted look while massive security arrangements were put in place to maintain law and order. Internet on mobile phones also remained suspended for the second day, a common practice by authorities to make organizing protests hard.
Describing Mohammad Rafi as "humane", "polite" and "caring", professor of global relations at University of Westminster, Dibyesh Anand said, "When he had approached me years ago during a visit to Kashmir University, he came across as the most humane, polite and caring (person)". Later Sunday, tens of thousands of people gathered for the funeral of the slain rebel leader, including at least a dozen armed militants who fired their guns in air to salute their fallen comrade.
Urging the people to continue adhering to the Joint Resistance Leadership program, the Mirwaiz said that this is a "time of do or die".
The protesters represented the Kashmir Traders and Manufacturers Federation and were led by their President Mohammad Yaseen Khan. "Kashmir is not an economic issue and can not be resolved through development", he said. India's federal government blames Pakistan for beating terror in Kashmir, even though Pakistan has accused India of all human rights abuses from Kashmiris.
The 26 years old Paddar was among the most wanted terrorists and had joined HM in 2015 after deserting the Lashkar-e-Toiba (LeT).