Malik Naveed Khan, police chief of Pakistan's North West Frontier province, of which Peshawar is the capital, said the crackdown on Saturday was "going on smoothly".
"There has been no resistance, so far," he said, speaking to Reuters news agency. "No casualties, so far."
The historic Khyber Pass, long known as a den for smuggling, is the main road link with Afghanistan and provides crucial supplies to US forces across the border.
Military sources told Al Jazeera that security forces were shelling suspected Taliban hideouts in the mountains and had already destroyed three observation outposts.
The operation prompted a swift response from Baitullah Mehsud, a senior pro-Taliban leader in Pakistan, who has reportedly called off peace talks with the government.
"The talks will remain suspended until the government stops talking about operations and attacks against us," Reuters quoted Mehsud as saying.
"The situation is such that [the Taliban] are all around Peshawar, they are on our doorstep"
Mahmood Shah, former security chief in the tribal regions
He said he suspected similar operations being ordered against Taliban groups elsewhere in the region.
A large military contingent is also reported to have reached the Jandula area in South Waziristan.
A Taliban-linked group said an offensive in the area would only create further problems.
"If the government thinks there is any issue to address, that should be resolved through talks not by the use of force," said Munsif Khan, spokesman for the Virtue and Voice organization. "We are ready for talks with the government."
Peshawar fears
There has been growing concern about threats to Peshawar from Taliban fighters. Two weeks ago, a Taliban force from Khyber entered the city and seized 16 Christians, before later releasing them.
Mahmood Shah, a former security chief in the tribal regions, said: "The situation is such that [the Taliban] are all around Peshawar. They are on our doorstep."
"The situation is like water flowing into a field and until you have some obstruction to stop it, you will drown. We are drowning."
Al Jazeera's Kamal Hyder said there was likely to be some reprisal from Taliban fighters because of the the military operation, such as rockets being fired at Peshawar.
Around 1,500 troops and police commandos were deployed along the Peshawar border with the Khyber tribal region and its suburbs to protect the city's more than 1m populace.
Mujeeb Khan, a senior local official, said a round-the-clock curfew was imposed in the Bara area bordering Peshawar, and heavy contingents of troops were blocking the main road into Khyber.
"All bazaars are shut, and residents have been asked not to come out of their homes," he said.
Yousuf Raza Gilani, Pakistan's prime minister, was in Peshawar on Saturday. However, he insisted his trip was not related to the military operation