The spokesman said the identities of the slain militants are being ascertained.
All the the millitants killed in the gun battle were said to close aide of slained Hizbul commander Burhan Wani.
Meanwhile, a Kashmir University statement said that the family members of one of the contractual lecturers in the Department of Sociology namely Dr Mohammad Rafi Bhat S/o Abdul Rahim Bhat R/o Chunduna Ganderbal have this morning reported to the university's chief proctor that he is missing since yesterday. However, these efforts did not yield any results.
For the government and armed forces, killing of Padder and Sheikh is a major breakthrough, which police say would destabilize the militant network in south Kashmir and also bring a temporary halt to the recruitment.
"We made repeated appeals to them through public address system to surrender".
A group of three to five militants believed to be enganged in a gunfight, the officer said.
Shopian Senior Superintendent of Police Shailendra Mishra used public address system to offer the terrorists an option to surrender.
Twenty persons, including 13 militants and three Army personnel, were killed as security forces launched "coordinated", multiple operations in Shopian and Anantnag in south Kashmir on Sunday, 1st April.
Five Kashmir militants, including a rebel university teacher, have been shot dead by Indian soldiers - triggering protests in which five civilians were killed.
A police official told PTI, "The search operation turned into an encounter after the hiding militants fired upon the forces, which was retaliated". One civilian is in critical condition and is shifted to Srinagar. He had received a bullet wound in his head, the hospital sources said. Asif was killed in firing by the troops on protesters in Badigam. Three bodies of terrorists recovered in a clean operation by Jammu and Kashmir Police and CRPF. "Of them, five have succumbed to injuries", the official said.