Story highlights The Pakistan Taliban say Prime Minister Nawaz Sharif turned Pakistan into a U.S. colony

They say they blame him for the death of their former leader, who died in a U.S. drone strike

The terrorist group vows revenge attacks, starting with Sharif's home province of Punjab

The group has chosen a new leader, who might be linked to the attack on Malala Yousafzai

The Pakistan Taliban has vowed to carry out revenge attacks on the national government after appointing a new leader following the death of their former chief in a U.S. drone strike.

The terrorist group's new leader, Maulana Fazlullah, is a longtime militia commander possibly linked to the assassination attempt on teenage activist Malala Yousafzai. His elevation to the head of the extremist organization was announced Thursday.

The grim warning to the Pakistani government came the same day from Asmatullah Shaheen, who served as interim leader before Fazlullah's appointment.

Shaheen said the group would seek revenge against Prime Minister Nawaz Sharif and his government for the death of former leader Hakimullah Mehsud, who was killed in a U.S. drone strike in northwestern Pakistan last week.

The initial focus of the attacks,he said, would be Punjab, Sharif's home province and political stronghold.

"All areas will come under attack but Punjab will come first," Shaheen said. Punjab is Pakistan's most populous province.

He blamed Sharif for turning Pakistan into a "colony" of the United States and for Mehsud's death.

Shaheen said that proposed peace talks with the government are now off the table.

There were never truly talks between the two sides, he said, and there never will be.

The Pakistani government didn't respond to requests from CNN for comment on the matter.

Fazlullah, the new leader, is yet to make his own public statement following his elevation.

JUST WATCHED Reports: Pakistani Taliban leader killed Replay More Videos ... MUST WATCH Reports: Pakistani Taliban leader killed 03:31

JUST WATCHED Peace talks to go ahead in Pakistan Replay More Videos ... MUST WATCH Peace talks to go ahead in Pakistan 03:38

JUST WATCHED FULL Amanpour Malala Interview Replay More Videos ... MUST WATCH FULL Amanpour Malala Interview 54:20

He 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 said Fazlullah is believed to be in Afghanistan and is also believed to have been ordering attacks in Pakistan from there.

Swat, in northwestern Pakistan, was where militants shot and wounded teen activist Malala in October 2012 as she was riding home from school in a van.

The Pakistan Taliban claimed responsibility for the attack, and the Pakistani Interior Minister at the time, Rehman Malik, linked Fazlullah to the attack on Malala.

Fazlullah is known as a hard-liner who broadcast fiery sermons and hard-line ideology via an extremist radio station, earning him the nickname "Mullah Radio." The station was shut down when he was pushed out of Pakistan.

The group's Central Shura Council picked Fazlullah, along with a new deputy leader, Sheikh Khalid Haqqani.