A police official was shot dead by terrorists in the main market area of Hazratbal in Srinagar late Thursday afternoon.
Police said militants fired several pistol shots from close range at sub-inspector Mohammad Jamal, who died on the spot.
Earlier in the day, militants seriously injured two paramilitary Central Reserve Police Force troopers.
Police said the attack took place in Koker Bazaar, adjacent to city centre Lal Chowk. Militants fired pistol shots from a close range at the two on-duty CRPF troopers.
"The two troopers were immediately taken to SMHS hospital, where attending doctors have described their condition as serious," said a police officer.
Police and CRPF troopers surrounded the city centre, where shoppers and pedestrians ran in panic after the shootout, and search operations were underway.
No group has yet claimed responsibility for the attacks.