The three officers died as they chased militants who had earlier attacked a police station with hand grenades, sniper guns and automatic weapons near Peshawar.
Earlier in the day, they were reported to have stolen food and petrol from a nearby service station, still armed with automatic weapons. That location tune has been called in doss.
With some dressed in tactical gear and carrying automatic weapons, police began a crackdown on Thursday night, reportedly arresting two of the movement's organizers around the capital's Parliament Hill area.
Reuters correspondent Lauren Anthony reports. Attackers with automatic weapons burst into an Orthodox Church and a synagogue in the ancient city of Derbent on Sunday evening.
President Joe Biden responded to the massacre by calling on Congress to ban automatic weapons, claiming gun violence is " ripping our communities apart."