Sources said a civilian identified as Asif Mir, 21, a resident of Rahmoo village in Pulwama district, was critically injured in clashes with security forces in Badigam village of Shopian where the encounter broke out today morning.
He said the identities of the slain terrorists were being ascertained.
In the initial firefight, one SOG personnel of Jammu and Kashmir Police, Anil Kumar, and army soldier of 44 RR were injured.
Rafi, a Ph.D in his discipline, was among five militants killed by security personnel at the Badgam area of Shopian, almost 80km from his house.
Bhat had gone missing on Friday where students organized protests and urged the authorities to trace the teacher who belonged to Chundian village of Ganderbal district that is close to Srinagar. Five civilians were killed, one a teenage boy, and at least 50 others were wounded, police and doctors said.
"Encounter concluded at Badigam Zainpora Shopian, five bodies of terrorists recovered". The report said that the Jammu and Kashmir police was monitoring all calls from the encounter site here and as soon as they realized that Bhat had made a call to his family, they got in touch with his father and asked him to persuade his son to surrender.
Dr Rafi joined militant ranks purportedly on Friday after he went missing. Thousands who came out in support of the militants shouted slogans calling for Kashmir's independence from India and threw stones at heavily-armed Indian forces.
Bhat's family informed university authorities about his disappearance yesterday morning, following which protests rocked the varsity campus over his disappearance.
Mr Bhat was reportedly meeting Hizbul commander, Saddam Padder, when security forces launched the operation. Their families were brought to the encounter site and repeated appeals were made through public address system to them to give up arms and hand themselves over to law "but in vain".
Internet services in the area were suspended in the aftermath of Sunday's killings, a Reuters witness said, and train services have been suspended.