While residents say all the four killed were civilians, Mir said three had no militancy record and were "obviously" civilians. The fourth person killed in Saturday's firing was a militant.
"Locals said he was a labourer from Bihar, but our channels say he was a militant," the IGP said.
The police chief said cases have been registered in both incidents.
Separatist leader Syed Ali Geelani called for a shutdown in the Kashmir valley and the Chenab valley districts of Kishtwar, Doda and Ramban Thursday over the killing of the man in Shopian.
Jammu and Kashmir Liberation Front chairman Muhammad Yasin Malik also called for a sit-in at the city centre Lal Chowk in Srinagar Friday.
Chief Minister Omar Abdullah chaired a high level meeting in Srinagar Wednesday evening to review the security situation in the town.
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