Constable Dalbir Singh was shot at by unidentified militants from a very close range at Rajpora chowk in Pulwama town, 35 km from here, around noon, police said.
Singh was referred to a hospital here in a critical condition, where he succumbed to injuries.
In Yaripora market of Kulgam district, 80 km from here, militants shot at constable Mukhtar Ahmad, who was posted on duty there, the police said.
Ahmad was rushed to district hospital Kulgam, where he was declared brought dead, police said adding the incident took place around 5.30 PM.
Soon after the attacks, operations were launched at both places to track down the assailants who fled the scene taking advantage of panic caused by the shootings.
No militant outfit has claimed responsibility for the attacks so far.