"Five terrorists have been killed so far in the operation that began on Friday evening in Kiloora village," Defence Ministry spokesman Colonel Rajesh Kalia told the media here.
Jammu and Kashmir Police chief S.P. Vaid tweeted: "Four more bodies of terrorists visible at encounter site (in) Kiloora, Shopian, taking the total to five terrorists killed. Good Job boys, good for peace."
The identities of the slain militants were not immediately known.
Director General of Police (DGP) S.P. Vaid said all five holed-up militants in Badigam village have been killed.
"Encounter concluded at Badigam Zainpora Shopian, five bodies of terrorists recovered. Well done boys - Army/CRPF/J&K Police," the DGP tweeted.
The slain militants have been identified as Saddam Paddar -- a top Hizbul Mujahideen commander, Tawseef Sheikh, Molvi Bilal, Adil Ahmad and Muhammad Rafi Bhat -- the missing Kashmir University assistant professor, who according to police had joined militant ranks.
Paddar was a close associate of Burhan Wani, who was killed in July 2016 in a gunfight in Kokernag area in Anantnag district.
Bhat was trapped along with militants in the gunfight.
Bhat, an assistant professor in the sociology department of Kashmir University, was reported missing on Friday. He belonged to Chunduna village in Ganderbal district.
Earlier, the police took his mother, wife and brother to Badigam village to persuade Bhat to surrender.
There were angry protests in the university campus on Saturday as students asked the authorities to locate Bhat.
Para commandos of the army were also deployed to help fight the holed up militants during Sunday's gunfight.
The security forces including Rashtriya Rifles (RR), Special Operations Group (SOG) and Central Reserve Police Force (CRPF) had surrounded Badigam following a tip-off about the presence of militants.
An army soldier and a policeman were also injured in the gunfight.
Besides, 12 civilians sustained injuries in the clashes between protesters and security forces near the gunfight site.
One civilian with critical injuries has been shifted to Srinagar for treatment.
Authorities have suspended mobile internet services across south Kashmir.
Sources in the Sher-e-Kashmir Institute of Medical Sciences (SKIMS) here said 19-year-old Rayees Ahmad admitted in the hospital on Saturday succumbed on Wednesday morning.
With this the death toll in Ganowpora village firing rose to three. Javaid Ahmad and Suhail Ahmad were killed in the army firing when a stone pelting mob attacked an administrative convoy of 10 Garhwal unit on Saturday.
Army said its personnel had fired in self-defence after a junior level officer fell unconscious following the mob attack.
Police has registered an FIR of murder against the soldiers of the unit.
The BJP has demanded withdrawal of the FIR while the Chief Minister Mehbooba Mufti said the investigation into the killings of the civilians would be taken to its logical conclusion.
A magisterial probe has also been ordered by the state government into the firing incident.
The bullet-riddled body of Lieutenant Ummer Faiyaz, who was posted with the Rajputana Rifles unit in Aknoor, was found in south Kashmir's Shopian on Wednesday.
Faiyaz was on leave and visiting his native place in Kulgam to attend a marriage in his family. He was kidnapped by militants late on Tuesday evening from Kulgam town, an official said.
Faiyaz had passed out from National Defence Academy, and was to go for the Young Officers' Course in September this year. He was also a hockey and volleyball player.
He was commissioned in the Army in December 2016.
"In a dastardly act some unidentified terrorists on Tuesday abducted and then killed a young, unarmed army officer, Ummer Faiyaz," Defence Ministry spokesman Colonel Rajesh Kalia said.
Jaitley said the government shared the grief of the family, adding that Faiyaz will continue to inspire youth in the valley.
"Abduction and murder of Lieutenant Ummer Faiyaz by terrorists in Shopian is a dastardly act of cowardice. This young officer from Jammu and Kashmir was a role model," Jaitley said in a tweet.
Jaitley said the officer was an "exceptional sportsman, his sacrifice reiterates nation's commitment to eliminate terrorism from the Valley."
"We share the grief of family of Lt. Ummer Faiyaz and stand in solidarity. Lt. Ummer Faiyaz will continue to inspire youth from the Valley," the Minister added.
Colonel of the Rajputana Rifles, and General Officer Commanding in Chief of the South Western Command Lt. Gen. Abhay Krishna said the perpetrators will not be spared.
In his condolence message, Krishna said the Army fraternity stood by the family and added: "I also assure the family that perpetrators of this heinous crime and dastardly act will not be spared."
"This marks a watershed moment in Kashmir valley, and people of Kashmir will decisively turn the tide against terrorism," he said.
Faiyaz had gone to attend the marriage of his maternal uncle's daughter at Batapura. He was abducted from there around 10 p.m. This bullet riddled body was found at Harmen, an Army source said.
The body has been sent for post-mortem at District Hospital in Shopian, and will be buried with full military honours.
An advisory was earlier issued by the state police asking its personnel not to visit ancestral homes, especially in south Kashmir areas till it was withdrawn.
There has been a spike in militant activity in most districts of south Kashmir including Pulwama, Shopian, Anantnag and Kulgam.
Tariq Ahmed, the driver belonging to Shopian district, had taken the family from Bhopal to the famous Aharbal falls four days ago.
After returning from the trip, the family forgot their bag in the vehicle.
"Tariq worked hard to trace the family and finally returned the bag that contained cash, gold and smartphones worth over Rs 10 lakhs," the Tourism Department sources said, adding that the family has expressed gratitude at Ahmed's noble and honest gesture.