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.