Mohammad Radmanesh, an Afghan Defense Ministry spokesman, said the drone strike occurred early Thursday shortly before the Afghan Taliban, responding to the government's cease-fire, started a three-day truce of its own to mark Eid al-Fitr, the Muslim holiday that follows the end of the holy fasting month of Ramadan.
The U.S. military said in Washington on Thursday it had carried out a strike aimed at a senior militant figure in the eastern Afghan province of Kunar, which is on the Pakistani border, and one U.S. official said the target was believed to be Fazlullah.
A USA official said the US believes that it is likely the strike killed Fazlullah, but efforts are ongoing to confirm his death.
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.
Since then, U.S. officials said, he directed numerous high-profile attacks against American and Pakistani targets.
A statement from US Forces-Afghanistan claimed that the strike didn't put at risk the ongoing and unilateral ceasefire initiated by the Afghan government.
In 2012, Fazlullah-led Pakistani Taliban shot teenager schoolgirl Malala Yousafzai in her hometown of Swat.
Fazlullah was killed in Afghanistan's northeastern Kunar province.
Fazlullah is likely behind several high-profile attacks, including the attempted assassination of human rights activist Malala Yousafzai.
According to Pakistani officials, Fazlullah, who is believed to be in his forties, took refuge in Afghanistan after the TTP was pushed out of Pakistan following a major offensive by the Pakistani military against the organization. Sources say that as soon as Fazlullah boarded the vehicle missiles fired from an unmanned American aircraft hit them.
U.S. Secretary of State Mike Pompeo echoed Ghani's remarks, saying peace talks would have to include a discussion on the role of "international actors and forces".
Although Pakistani Taliban militants still unleash attacks, the group has lost control of all territory in Pakistan since its December 2014 attack on an army school that killed 132 children.
However, the Associated Press reported, Sakhi Mashwani, a lawmaker from Konar province, said five other insurgents were killed. Washington, for its part, accuses Islamabad of providing safe havens to the powerful Haqqani network, a group involved in numerous brazen attacks on foreign forces in the war-ravaged country in recent years.