Jamil Khan says five soldiers also died in the battle on Tuesday. He says the fighting broke out when insurgents ambushed security forces during a routine search in the Orakzai region.
He says several militants were also wounded in the fighting.
Khan is the administrator for Parachinar, the capital of the neighboring tribal agency of Kurram. The remoteness of the Orakzai tribal region makes it impossible to verify the government's accounts.
Orakzai has seen intense battles between the army and militants in recent years.