Hundreds of lorries and containers have been destroyed in a number of attacks around the city in recent weeks.
In the latest attack on Wednesday, a woman was killed and her two children wounded when three missiles were fired at a Nato supply convoy.
"Militants fired three missiles on Afghanistan-bound trucks carrying supplies for Nato forces. Two landed in open space and one hit a house, killing a woman and injuring two children," Bakhtiar Mohmand, a local government official, said.
About 75 per cent of the vehicles, parts, weapons, fuel, water and food needed to sustain more than 60,000 foreign troops in Afghanistan moves through the pass and a second overland route to the south between Quetta and Kandahar.
On Tuesday, armed men attacked a fuel tanker on the southern routeHauliers' threat
Earlier in the week, hauliers in Pakistan said they had stopped transporting the supplies due to the attacks.
Nato forces say the deliveries have continued with about 170 lorries crossing the border on Tuesday, but local drivers are concerned about the increase in violence.
"The militants cannot differentiate between Nato and local supplies when they see a container on the back of a truck they open fire and may even kill you," one driver told Al Jazeera.
Admiral Giampaolo Di Paola, the head of Nato's military committee, said on Tuesday that the military alliance was looking to diversify its supply routes.
He said that progress was being made on agreement to allow non-lethal equipment to be brought in with Russian help.
"We are looking to open multiple routes of communication," he said, noting that talks with Turkmenistan were also advancing.
"The more lines, the better."