An early-morning call on Sunday by the police to the family at Ganderbal's Chanduna sought their help in persuading Bhat to surrender.
A police officer also confirmed the killings and said that it is being investigated under what circumstances they were killed.
Witnesses said government forces fired tear smoke shells, pellets and bullets to disperse the stone throwing protesters, leaving many of them wounded.
"Tomorrow as the "Durbar" [court] of our killers opens in Srinagar, leadership and people from all walks - traders, lawyers, students, employees and others will move towards civil secretariat and will sit in a peaceful dharna [sit-in] till the daily carnage is not stopped".
Some Kashmiri groups in Jammu and Kashmir have been fighting against Indian rule for independence, or for unification with neighboring Pakistan. He completed his PhD previous year.
On Saturday, Indian troops killed three suspected rebels during a gunbattle in Srinagar, while one civilian was martyred when a police armored vehicle ran over him during clashes with government forces.
Sunday was the second straight day of unrest in the region.
Mobile Internet services also remained suspended for the second day in the region.
Todays encounter in Badigam comes within 24 hours of a swift police operation in Chattabal area of the city in which three Lashker-e-Taiba militants were gunned down.
Dozens of protesters have been injured in forces action during clashes near the encounter site.
More than 270 rebels have been killed in intensified operations led by the Indian army since past year, officials say.
Five terrorists were killed in an encounter at Badigam in Shopian's Zainpora.
Reports identified the slain terrorists as Saddam Padder, Mohammad Rafi Bhat, Tawseef Sheikh, Bilal Moulvi and Adil Ahmad. Among those slain was a university assistant professor.
Police made repeated attempts to make them surrender which did not materialise, the official said.
SSP Shopian Shailendra Kumar Mishra appealed to the militants to surrender but they spurned the offer and preferred to fight. We even brought the university teacher's father all the way to Shopian.
Anti-India protests and clashes continued in the area and also spread to some other towns and villages of southern Kashmir.
Opposition National Conference (NC) working president Omar Abdullah said Kashmir issue has to be resolved through sustained dialogue and engagement and the "unabated" civilian killings in the Valley were unacceptable.
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