Mahmood Khan Achakzai, a renowned Pushtun leader, made the request for the extradition on behalf of Prime Minister Nawaz Sharif when he met Afghan President Hamid Karzai in Kabul on Wednesday, The Express Tribune reported.
The foreign office confirmed that Achakzai, accompanied by foreign secretary Aizaz Ahmed Chaudhry, visited Afghanistan as a special envoy of the Prime Minister to seek Kabul's cooperation against terrorism.
A government official familiar with the development said that Pakistan asked Karzai government to stop supporting the TTP and extradite its fugitive chief hiding in Afghanistan.
The official said that Pakistan had compelling evidence suggesting that Mullah Fazlullah and other TTP commanders were enjoying "patronage" of Afghanistan's intelligence agency.
It was decided that an Afghan delegation would also soon visit Islamabad to carry a special letter from President Karzai that would list some proposals and would also discuss future plans with Pakistani side, the paper said.
Fazlullah, nicknamed the "Mullah Radio", became the TTP chief in November last year after the killing of his predecessor Hakimullah Mehsud in a US drone attack.
During the weekly briefing at the Foreign office yesterday, spokesperson Tasnim Aslam said that Afghan authorities had assured their cooperation to Pakistan.
Following Achakzai's visit to Kabul, Afghan President Karzai telephoned Prime Minister Sharif and discussed the anti-terror cooperation between the two neighbours.
"Sharif agreed with all parts of an Afghan that both countries should jointly fight with all terrorists. Safe havens of terrorists should be dismantled and there should be a road-map to coordinate the joint struggle," a statement from Karzai's office said.
Pakistan has launched a massive operation against Taliban in the North Waziristan but there is increasing worry over reports that militants are easily crossing over towards Afghan side and taking shelter there.
Pakistan has asked Afghanistan to seal common borders to stop the escape of militants from Pakistani territory.