Councillor Riyaz Ahmad Peer and special police officer (SPO) Shafqat Nazir Khan succumbed to gunshot wounds at a local hospital and a civilian, Shams-ud-din Peer, who was injured in the attack on the Sopore Municipal Office, was transferred to a hospital, said the police statement.
The statement said the area, once a hotbed of militancy, has been cordoned off and a search operation launched to find the attackers.
In the absence of an elected government -- Kashmir is currently being ruled directly by New Delhi via a lieutenant governor -- local elected bodies like municipal and district development councils have taken a center stage in governance.
The elections for the District Development Councils in December last year are being projected by the ruling Bharatiya Janata Party (BJP) Indian government as an endorsement of its Aug. 5, 2019 decision, when Jammu and Kashmir was stripped of autonomous status and downgraded from a full-fledged state to a centrally governed territory.
Several Kashmir-based pro-India political parties have accused the BJP of coercion and intimidation to tilt the results for the final composition of these councils in its favor.
Kashmir is held by India and Pakistan in parts and claimed both in full. A small sliver of Kashmir is also held by China.
Since they were partitioned in 1947, the two countries have fought three wars -- in 1948, 1965, and 1971 -- two of them over Kashmir.
Some Kashmiri groups in Jammu and Kashmir have been fighting against Indian rule for independence, or unification with neighboring Pakistan.
According to several human rights organizations, thousands of people have reportedly been killed in the conflict in the region since 1989.