Pakistan, however, denies the charge, and itself accuses the US of turning a blind eye to militants who attack Pakistani forces and civilians from Afghan soil.
A USA military spokesman, Lt. Col. Martin O'Donnell, said US and North Atlantic Treaty Organisation forces continue to adhere to a unilateral, week-long cease-fire declared last week by Afghan President Ashraf Ghani.
President Ashraf Ghani extended a government ceasefire on Saturday and urged the Taliban to do the same, garnering praise at home and global backing, but critics said such overtures have allowed the Taliban to pour into cities unchecked and win the upper hand. He expressed hope for its extension.
Mullah Fazlullah and his four commanders - identified as Abu Bakar, Sajid, Umar, and Imran - were killed in the USA drone strike in the Dangam district of the Afghan province of Kunar, near the Pakistan border.
He said the target was "a senior leader of a designated terrorist organization", but he did not offer further details or confirm that Mr. Fazlullah had been killed.
Radmanish said the attack took place in Marawara district, near the border. Lately, Washington and Islamabad had started cooperation to persuade Taliban for peace talks with Kabul.
Meanwhile, in his conversation with Ghani, Mulk said that Fazlullah's death would be received throughout Pakistan with relief as Pakistanis had borne the brunt of terrorist attacks by the Tehrik-e-Taliban Pakistan, which Fazlullah headed.
Pentagon officials say a US drone has targeted the leader of the Pakistani Taliban in an Afghan province near the border with Pakistan, and security sources as well as an Afghan official say he was killed.
Over the weekend, ecstatic men and children crowded around the soldiers and Taliban fighters, some of whom had checked in their weapons at the entrances to cities, and urged them to turn their ceasefire into a permanent peace.
He was designated a global terrorist by the USA and carried a bounty of $5 million.
He first rose to prominence inside Pakistan's Swat valley with fiery radio tirades that earned him the nickname Mullah Radio.