The official said more than 100 militants had also been killed, but the death toll was not possible.
The clashes signalled a fresh military push in the Tirah valley of Khyber district, where the military has been targeting Taliban and militia Lashkar-e-Islam who threaten the nearby northwestern city of Peshawar.
Khyber straddles the NATO supply line into Afghanistan, used by US-led troops to evacuate military equipment ahead of their 2014 withdrawal, and officials say it is key to protecting security in Peshawar for elections next month.
"Thirteen soldiers have died over the past three days in different parts of Tirah valley. Ground forces have intensified operations against TTP (Tehreek-e-Taliban) and Lashkar-e-Islam," a military official told AFP.
The official said more than 100 militants had also been killed, but the death toll was not possible to verify independently as the area is cut off to journalists and aid workers.
He said the town of Tut Sar had been "captured" back from militants and that soldiers had now erected a post in the area.
"Helicopters and jets participated in the operation. They are shelling militant hideouts in the valley," the official said.
A second military official confirmed the same details.
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