Tehreek-i-Taliban Pakistan spokesperson Ihsanullah Ihsan said four suicide bombers carried out the attack to avenge the killings of Baitullah Mehsud and Osama bin Laden, Express News reported.
Ihsan said the attackers succeeded and delivered a "lethal blow."
The air force said in a statement the seven or eight militants were equipped with rocket-propelled grenades and automatic weapons. The operation lasted about five hours.
The air force also said six militants were wearing suicide jackets and that one militant detonated his vest while hiding.
Eight suspects were arrested during during a search of nearby residential areas, Express News said.
A number of improvised explosive devices were found during the search, the air force statement said.