Pakistan's army chief met Afghan President Ashraf Ghani in Kabul in the aftermath of the school attack in the Pakistani city of Peshawar which killed 149 people, mainly children.
The army chief sought Ghani's support in defeating the Tehreek-e-Taliban Pakistan (TTP).
TTP leader Mullah Fazlullah is believed to be hiding in Afghanistan's Kunar province, which borders Pakistan's restive tribal areas.
Kunar has been the scene of fierce fighting between local forces and the Afghan Taliban for the past 10 days.
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"So far in the operation, 21 armed insurgents have been killed and 33 others wounded," Waziri said, adding that seven security personnel were wounded.
Kunar governor Shujaul Mulk Jalala said more than 1,500 Afghan Taliban fighters attacked remote villages in Dangam.
Jalala said Pakistani Taliban and Lashkar-e-Taiba militants were also battling Afghan security forces in Dangam.
Pakistan has repeatedly asked Afghanistan to capture and hand over Fazlullah.
Each nation has long accused the other of allowing militants to shelter in the border region and launch bloody attacks that threaten regional stability.
A follow-up mission of about 12,500 US-led NATO troops will stay on to train and support Afghan security forces.