The main fighting is in the Jamrud sub-district of Khyber
Pakistani forces have arrested 40 people and destroyed suspected militant houses and camps in a key operation in the Khyber region, officials say.
The operation has led to the closure of a crucial overland route carrying supplies to US and Nato troops fighting the Taleban in Afghanistan.
The offensive involves ground troops, helicopters and tanks.
There has been a spate of hijackings and attacks on vehicles carrying supplies into Afghanistan.
The top administrator of the Khyber tribal region, Tariq Hayat, told the BBC: "The security forces have arrested at least 40 suspected militants and criminals since Tuesday morning.
"Many of the arrested persons are local Taleban commanders and their sponsors. The forces have destroyed their houses."
Mr Hayat said 18 houses and at least 14 camps of Taleban militants in the region had been destroyed.
The section of the Khyber Pass that passes through the Jamrud sub-district is the most insecure stretch of the road.
Witnesses told the BBC that the security forces were using artillery fire and helicopter gunships to pound suspected militant positions in the Ghundai and Shahkas areas of Jamrud.
The entire sub-district is under curfew.
Local officials said they did not know when the supply route would reopen but hoped it would be soon.
The international forces in Afghanistan have praised the Pakistan offensive despite the fact that the route carries about 75% of their supplies via Karachi.
US military spokesman in Afghanistan, Col Greg Julian, said: "We are glad that they're helping clean out what they call miscreants... Temporary closure is not a problem. It's best that they conduct this operation and clear out these trouble spots."
The offensive has closed the supply route to Afghanistan
However there have been reports Nato and the US are trying to find alternative routes through central Asia.
The offensive was a surprise move to many as there had been reports Pakistan was scaling down operations in the north-west to move some troops to the Indian border amid tension over the Mumbai attacks.
Since September the Taleban in Pakistan have targeted vehicles carrying supplies for foreign forces in Afghanistan.
They have hijacked lorries, stolen their cargo and kidnapped their drivers.
Some lorry drivers recently suspended organised convoys to Afghanistan because of the worsening security although some supplies did continue under heavy paramilitary guard.
Recently thousands of protesters turned out in Pakistan's city of Peshawar to demand an end to the supply route.