Hayat confirmed Pakistani security forces had launched "an operation against militants and armed groups in Jamrud" - the gateway to the Khyber Pass.
Pro-Taliban fighters have carried out a string of attacks in recent months aimed at choking off supplies transported to foreign forces in landlocked Afghanistan through northwest Pakistan.
Hundreds of Nato and US-led coalition vehicles were destroyed in a series of raids earlier this month.
"This is a giant operation. It will continue until we achieve our objective," Hayat said, adding that the operation could be extended beyond the Jamrud region if deemed necessary.
Alongside putting a stop to attacks on Nato and US supply vehicles, Hayat said the operation had been launched to tackle a spate of kidnappings for ransom in the tribal belt that straddles the Pakistan-Afghan border.
Hayat said: "We have 26 targets, we will eliminate their [pro-Taliban and al-Qaeda fighters] hideouts."
Two weeks ago, several haulage companies in Pakistan refused to undertake journeys along the 50km route, saying the security of their drivers could not be guaranteed.