Sardar Khan, a local police official, said two spells of aerial bombing destroyed about 40 houses in several villages.
He said bombs also struck a school occupied by Taliban fighters in Loi Sam, a village that has been a key focus of the fighting.
“Fighting is still continuing and forces backed by helicopter gunships are targeting pro-Taliban fighters’ positions mainly on the mountains. We have reports of over 100 militants dead,” said a spokesman for Pakistan’s Frontier Corps.
Kamal Hyder, Al Jazeera’s Pakistan correspondent, said: “A large number of people are said to be now leaving the area of Bajuar – where there has been intense fighting between government para-military forces.
“However, on the other side, the so-called Taliban elements – as they’re called out here in this area – have been showing determination against the security forces … If you look at what the so-called Taliban are saying – they’ve inflicted heavy casualties againt the Pakistani military.”
An Associated Press reporter in Khar, the main town in Bajaur, reported Taliban fighters patrolling and staking out positions with rocket launchers, heavy machine guns and, in some places, anti-aircraft guns.
Pakistan is under US pressure to crack down on the Taliban fighters in its tribal areas, from where they are said to launch attacks on government and Nato forces in Afghanistan.
The Bajaur offensive came in the wake of an assault by pro-Taliban fighters on Wednesday on an outpost manned by security forces.
Officials said those initial clashes killed 25 fighters and two troops, but conflicting casualty figures were reported on Sunday.
A military intelligence official, speaking on condition of anonymity because he was not authorised to speak to the media, placed the number of troops dead at 13.
Maulvi Umar, a Pakistani Taliban spokesman, claimed fighters had handed over 22 bodies belonging to security forces in the last three days after pleas from tribal elders.