All six of those killed in the offensive in the Khyber region were "terrorists", the military said in a statement late Sunday.
The army launched air and ground operations in the Rajgal valley, about 90 km (60 miles) west of the city of Peshawar, last week, the latest leg of an offensive against the Pakistani Taliban and its allies that began in 2014.
Pakistan has for years been battling militants, while quietly backing others who are seen as furthering Pakistani objectives against old rival India and in Afghanistan.
The Pakistani offensive has squeezed some groups into small pockets of territory, while others have fled over the border into lawless areas of eastern Afghanistan.
Nevertheless, the militants are still capable of launching deadly attacks across Pakistan, Reuters reported.
A bomb attack on a crowd in a hospital courtyard in the city of Quetta on Aug. 8 killed more than 70 people, the deadliest attack in Pakistan since 2014.
The military says it has killed at least 31 people in coordinated ground and air strikes in the Rajgal area since Aug. 16.
The attacks would "effectively check and guard against terrorists’ movement along high mountains and all-weather passes", the army said.
Pakistan and Afghanistan have accused each other repeatedly of not doing enough to stop the movement of militants across the border.
Pakistan has been battling the Pakistani Taliban, an umbrella organization of hardline terror groups, since its inception in 2007.
The Pakistani Taliban are allied with but separate from the Afghan Taliban.