The skirmishes took place in the Sarakai and Mukha areas northwest of Khar, the main town of Bajaur district where Pakistan has carried out a series of offensives against Taliban and other insurgents since August 2008.
"A group of militants attacked security forces and local lashkar (militia) during a joint search operation in the two areas, triggering a gunfight," local government official Mohammed Ilyas Khan told AFP.
He said that at least 11 militants and one member of the lashkar were killed in the clashes.
Khan said he did not know the nationality of the militants killed but said they had been hiding since Thursday's attack on a village in Bajaur.
Local security officials confirmed the clashes and casualties.
Earlier this month, Pakistan conveyed "strong concern" to the Afghan ambassador to Islamabad, calling for "stern action" by Afghan and US-led NATO troops to crack down on militants in eastern Afghanistan.
Copyright AFP (Agence France-Presse), 2011