Just after an hour they killed two policemen in Zadibal area of Srinagar on Monday, militants struck again in Tengpora by-pass area where they killed another policeman and snatched his service rifle.
Hizbul Mujahideen has claimed responsibility for both attacks.
"Militants fired at the personal security guard of a protected person in Tengpora area of Srinagar city," a senior police officer said.
"The injured policeman later succumbed to bullet injuries. The militants also snatched the service rifle of the policeman," the officer added.
Earlier in the day, motorcycle-borne assailants killed an assistant sub-inspector (ASI) and a constable near the mills in Zadibal area of city.
Two policemen were regulating traffic during the rush hour in the area and were unarmed when the militants attacked them.
Monday's attacks in Srinagar city are the first major strikes carried out by the militants after the Mehbooba Mufti-led Peoples Democratic Party and Bharatiya Janata Party formed a coalition government in Jammu and Kashmir.