The air strikes came after a militant hostage siege at army headquarters near Islamabad left 19 people dead at the weekend, and as the military prepares for an offensive in the tribal region bordering Afghanistan.
"Jet fighters bombed various Taliban hideouts in Mamoond district of Bajaur," local government official Manasib Khan told AFP, referring to a district north of the provincial capital Peshawar.
"The latest reports said that at least 12 militants were killed and nine were wounded in the air strikes," he said, adding that Taliban trenches on mountaintops and underground hideouts were targeted by the war planes.
"Ground troops are also using artillery to pound militant positions in Mamoond area," Khan said.
An intelligence official at Khar, the main town in Bajaur, confirmed the air strikes and death toll.
Fighter jets also bombed Taliban strongholds in South Waziristan, the semi-autonomous tribal district believed to be the target of an upcoming operation against the Tehreek-e-Taliban Pakistan network linked with Al-Qaeda.
"Pakistan fighter jets bombed hideouts at Makeen and Ladha towns," Syed Shahab Ali Shah, the area´s top administrative official, told AFP.
A security official in South Waziristan´s main town Wana said: "We have reports that at least 19 militants were killed in both Makeen and Ladha."
The army claimed success in an offensive against the Taliban earlier this year in the one-time tourist paradise of Swat valley, but a wave of attacks in the past week show the Islamist threat is far from quashed.
Military and government officials have been saying for months that a full operation is imminent in the tribal belt, but have given no timescale.
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