"Well done boys - Army/ CRPF/J&K Police", DGP S P Vaid tweeted.
Paddar was killed with four other suspected militants, including a sociology professor at the University of Kashmir, in an encounter at Badigam in south Kashmir's Shopian.
Four civilians were also injured as security forces opened fire at a mob that indulged in stone-pelting.
The clashes erupted after five terrorists, including Hizbul commander Saddam Paddar, Kashmir University assistant professor Muhammad Rafi Bhat, Tawseef Sheikh, Molvi Bilal and Adil Ahmad, were killed in the Shopian gunfight.
A policeman and a soldier of 44 Rashtriya Riffles were also injured in the encounter.
The father, Fayaz Ahmed Bhat, accompanied by Rafi's mother, sister and wife left their residence in Chundana in Ganderbal to reach the encounter site. "Meanwhile, police made repeated attempts to make the hiding terrorists surrender". Soon after the encounter started, clashes broke out in which five civilians were killed.
Three security personnel were injured and were undergoing treatment at a hospital, officials said. "I will remember your love and respect", he wrote, adding, "Allah bless you all". Security forces in their guarded response fired back, " a police spokesman said.
According to police, the gunbattle with militants began early Sunday morning in Badigam village of Shopian.
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Padder and his aides were involved in a number of civilian killings and attacks on security forces besides instigating youth to join the terrorist network, police said.
Chunduna, Ganderbal: Among thousands of mourners, more than a dozen students sat in a line, waiting for the dead body of professor Mohammad Rafi Bhat to arrive in Chunduna village of Central Kashmir's Ganderbal district on Sunday evening.
The Kashmir University has cancelled all academic activity for two days and postponed the exams scheduled to be held today.
She said today's deaths have brought a stark fact to fore that gun, either way of a militant or that of security forces, is no solution for resolving issues.
Dr Saleem Tak, superintendent of Shri Maharaja Hari Singh hospital, told Al Jazeera one of the dead civilians suffered a bullet wound to the head.
In a statement, the business fraternity said that Kashmir was a dispute and needs to be resolved for sustainable peace in the subcontinent.
Authorities imposed restrictions under section 144 of the CrPc in parts of Srinagar as a precautionary measure to maintain law and order in view of a strike called by separatists over the killing of militants.
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