Officials said those initial clashes killed 25 fighters and two soldiers.
Details of the renewed fighting on Friday were scarce.
But the death toll rose among government forces to seven, according to an army official and a Peshawar-based intelligence official who spoke on condition of anonymity because they were not authorised to speak to the media.
The army official said 30 militants were killed, while the intelligence official said 40 fighters died and at least 25 were wounded.
The latter said fresh paramilitary troops were advancing toward Loi Sam, a village that has been a main scene of the fighting.
Major-General Athar Abbas, the army spokesman, said only helicopters were operating in support of paramilitary troops on the ground.
Residents in Bajaur's main town of Khar said they had seen the helicopters in the air and heard the sound of mortar fire.
"Intense fighting is going on between soldiers and Taliban since Friday morning," said Sher Zamin, a local resident.
He said he saw Taliban fighters going towards the scene of the clashes.
Pakistan is under growing US pressure to crack down on armed groups in its tribal areas, from where they launch attacks on government and Nato forces in neighbouring Afghanistan.
Bajaur is also considered a possible hiding place for al-Qaeda leaders Osama bin Laden and Ayman al-Zawahri.