The release of the 40-minute video follows three high-profile Taliban attacks in the northern city of Peshawar this month: an attack by multiple suicide bombers on the airport, the killing of a senior politician and eight others in a bombing, and the kidnap of 22 paramilitary forces on Thursday.
The attacks underline the Taliban's ability to strike high-profile, well-protected targets even as the amount of territory it controls has shrunk and its leaders are picked off by US drones.
"We believe in dialogue but it should not be frivolous," Hakimullah Mehsud said. "Asking us to lay down arms is a joke."
In the video, Mehsud sits cradling a rifle next to his deputy, Wali ur-Rehman. Military officials say there has been a split between the two men but Mehsud said that was propaganda.
"Wali ur-Rehman is sitting with me here and we will be together until death," said Mehsud, pointing at his companion.
Pakistani officials did not immediately respond to calls seeking comment.
The Taliban said in a letter released Thursday that they wanted Pakistan to rewite its laws and constitution to conform with Islamic law, break its alliance with the United States and stop interfering in the war in Afghanistan and focus on India instead.
Mehsud referred to the killing of the senior politician in his speech and said the political party, the largely Pashtun Awami National Party, would continue to be a target along with other politicians.
"We are against the democratic system because it is un-Islamic," Mehsud said. "Our war isn't against any party. It is against the non-Islamic system and anyone who supports it."
Pakistan is expected to hold elections next spring. The current government, which came to power five years ago, struck an uneasy deal with the Taliban in 2009 that allowed the militia to control Swat valley, less than 100 km (60 miles) from the capital, Islamabad.
A few months later, the military launched an operation that pushed the militants back. The US military also intensified its use of drone strikes.
Now the Taliban control far less territory and the frequency and deadliness of their bombings has declined dramatically.
The Taliban's key stronghold is in North Waziristan, one of the tribal areas along the Afghan border and the site of most of the hundreds of drone strikes by the United States.
Mehsud said in his interview that although he was open to dialogue, the Pakistani government was to blame for the violence because it broke previous, unspecified deals.
"In the past, it is the Pakistani government that broke peace agreements," he said. "A slave of the US can't make independent agreements; it breaks agreements according to US dictat."
Mehsud said that the Pakistan Taliban would follow the lead of the Afghan Taliban when it came to forming policy after most NATO troops withdraw from Afghanistan in 2014.
"We are Afghan Taliban and Afghan Taliban are us," he said. "We are with them and Al Qaeda. We are even willing to get our heads cut off for Al Qaeda."