The group said in a statement that its fighters carried machine guns, grenades and assault rifles during the hour-long gunbattle, but that none of the militants were hurt.
Researchers say the idea is to replace explosives in small hand grenades with a certain variety of red chilli to immobilise people without killingthem.
High-rankers in this clan love to don military trappings, such as medals, eagle-wing or axe cap-badges, binoculars, monocles, and bandoliers festooned with grenades.
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.