Fazlullah was elected to lead the Pakistani Taliban in 2013 after the death of his predecessor, Hakimullah Mehsud, in a USA drone strike.
The strike early Thursday morning in northeastern Kunar province killed Fazlullah and two other insurgents, an Afghan Defense Ministry spokesman told the AP Friday.
But he said the the ceasefire "does not include USA counterterrorism efforts" against other armed groups in the region.
In 2014, she was awarded the Nobel Peace Prize jointly with Kailash Satyarthi for activism on behalf of children's rights.
US forces had conducted the strike close to the border of Pakistan, targeting the "Emir" of the group, according US Forces-Afghanistan spokesman Lt. Col. Martin O'Donnell.
Fazlullah, one of the Pakistan Taliban's longtime militia commanders, was elected leader in 2013.
This includes the December 2014 attack on the Army Public School in Peshawar, which killed 151 people.
In 2012, its fighters also shot Malala Yousafzai, then an 11-year-old who advocated education for fellow girls. The TTP accused the Afghan intelligence service NDS, which has always been suspected by Pakistan of harbouring Fazlullah, of providing information for the drone attack.
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"We targeted (Fazlullah) but we're not ready to call jackpot yet", a USA defence official told AFP.
Unconfirmed reports from locals said Fazlullah has been killed, the Voice of America reported.
The tribes are fiercely independent and despite the Pakistani army's claims they were going after foreign fighters fleeing the war in Afghanistan, the backlash against the Pakistani government led to the formation of a branch of the Taliban.
There was no official confirmation from Pakistan, but a Pakistani senior security source told AFP that Fazlullah is believed to have been killed. "They were staying at a house when the drone fired missiles and martyred them", said Taliban member Maulvi Abdur Rasheed.
They are separate from the Afghan Taliban who ruled Afghanistan for five years until they were ousted in 2001 by United States military action following the 9/11 terror attacks.
There are differences between the Pakistan and Afghanistan Taliban, notably in their origins but also in outlook.
Mulk made the comment in a telephone conversation Friday night with Afghan President Ashraf Ghani and thanked him for sharing information about Fazlullah's killing, said a Pakistan government statement.
Pakistan has always been accused of supporting the Afghan Taliban and providing safe haven to its leaders - charges Islamabad denies.