Twenty-one suspected militants and eight soldiers were killed on Wednesday, the military said in a statement, but gave no figure for civilian casualties.
National disaster officials say the fighting has forced more than 18,000 people to abandon their homes.
Residents of the area say many people are caught between the two opposing forces, as the military orders them to leave and the militants urge them to stay.
“Security forces were asking us to leave their area as there would be heavy bombing against the militants,” said one villager, Muddasir Shah.
But the militants had set up bunkers and were patrolling villages to prevent residents from leaving, he added. “The militants were saying we shouldn’t flee the villages. We don’t know whom we should trust.”
The military said it had killed dozens of militants in airstrikes and fighting since the fighting began in Khyber.
“The militants wanted people not to leave their houses so that the military don’t use fighter jets and artillery against them,” said Khair Zaman, 47, who had spent nine hours wandering on unfrequented back roads moving his family to safety.
On Sunday, the military said it had killed 18 militants in airstrikes.
The Khyber offensive began two weeks ago in the area around the Tirah Valley, a key smuggling route into neighboring Afghanistan. At the same time, the military is pressing on with a campaign against the Taliban it launched in nearby North Waziristan in June. -Reuters