Fifteen members of the local anti-Taliban militia were also injured in the clash. The Associated Press quoted at least 13 militants being killed in the clash.
Encouraged by Islamabad, the tribesmen recently formed the militia to kill or evict Taliban militants and their supporters from the region.
They have killed 25 insurgents in clashes this week.
Kurram is located near Afghanistan. The Pakistani military also has carried out several offensives against Taliban who are hiding in the area after escaping last year’s offensive in the nearby Orakzai tribal region.