The spokesman for the United States military in Afghanistan, Lt. Col. Martin O’Donnell, confirmed that the military had carried out a drone strike on Wednesday in Kunar. 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.

Mr. Fazlullah has been the most-wanted militant in Pakistan for years. His organization has carried out hundreds of attacks against both Pakistani security forces and civilians, including an assault on a school in Peshawar in 2014 that killed 145 people or more, including at least 132 children.

In 2012, a Pakistani Taliban gunman shot Malala Yousafzai, a teenager who had been calling for more educational opportunities for girls. Ms. Yousafzai survived and received the Nobel Peace Prize in 2014.