Pakistani war planes bombarded militant hideouts in Orkazai Agency on Sunday, killing 16 militants and wounding many others Press TV reported.
Security forces also pounded militant positions in different areas of Kurram Agency, killing 20 militants and injuring 18 others.
The operation was carried out after the militants ambushed a security checkpoint in the tribal region.
Meanwhile, unknown militants blew up a primary school in Mardan district of northwestern Khyber Pakhtunkhwa province on Sunday as government troops were engaged in battles with militants in the tribal region bordering Afghanistan.
Suspected pro-Taliban attackers managed to escape the scene.
There were no reports of casualties since the school was empty at the time of the attack, local officials said.
Over the past several years, the militants have destroyed hundreds of schools, especially in Khyber Pakhtunkhwa province, previously known as North-West Frontier Province.