Maulana Fazlullah, the cleric named to lead Pakistan Taliban, said Pakistani Prime Minister Nawaz Sharif turned the country into a U.S. "colony" and vowed revenge, starting in Sharif's home province of Punjab, CNN reported.
Hakimullah Mehsud was killed in a U.S. drone strike in northwestern Pakistan.
The warning to the Pakistani government came from Asmatullah Shaheen, who was interim leader before the appointment of Fazlullah, who may be linked to the assassination attempt on teen activist Malala Yousafzai.
"All areas will come under attack but Punjab will come first," Shaheen said.
Shaheen blamed Sharif for Mehsud's death and said proposed peace talks with the government would no longer be considered, CNN said.
Fazlullah once led a Pakistan Taliban militia in the country's Swat region. The Pakistani military drove Fazlullah's group out of Pakistan in 2009, forcing it to operate from Afghanistan.
Pakistani military sources told CNN Fazlullah is believed to be in Afghanistan and ordering attacks in Pakistan from the neighboring country. However, Dawn newspaper reported it appeared Fazlullah recently returned to Pakistan.
Fazlullah, whose militants shot and almost killed Malala in October 2012 for advocating education for women and girls, was known as "Mullah Radio" for his radio broadcasts to preach Sharia laws during his days in the Swat Valley in Northwest Pakistan.
Sharif, who was elected prime minister in May, has been seeking to open peace talks with Taliban Pakistan to try to end violence that has resulted in the deaths of hundreds of people.
The drone attack that killed Mehsud was widely condemned in Pakistan, with some officials saying it had sabotaged peace talks. Sharif's government, however, has said it will pursue the dialogue process with the Taliban to prevent further bloodshed.