Mohammad Radmanesh, deputy Defense Ministry spokesman in Kabul, told Anadolu Agency that Fazlullah - wanted under the U.S. State Department's Rewards for Justice since this March - was killed in a drone strike carried out two days ago.
A USA official said the US believes that it is likely the strike killed Fazlullah, but efforts are ongoing to confirm his death.
A Pakistan military spokesman later said Bajwa's discussions also focused on "measures needed to check rise of ISIS (Islamic State) and the issue of terrorists taking benefit of the porous border to indulge in terrorism, smuggling and drug trafficking, being often networked together".
Officials have in the past said Fazlullah directed numerous high-profile attacks against USA and Pakistani targets over the years.
However, he noted that the cease-fire applies to the Afghan Taliban and "does not include USA counterterrorism efforts" against a local branch of the Islamic State, al-Qaida "and other regional and worldwide terrorist groups".
Pakistani Taliban leader Mullah Fazlullah has been killed in a U.S.
"Mullah Fazlullah's death is huge news", tweeted Omar Waraich, deputy South Asia director for Amnesty International.
The US strike comes amid a ceasefire between the Afghan Taliban and Afghna security forces to mark the end of the Muslim's holy month of Ramazan.
The group was behind the massacre of more than 150 people at a Peshawar school in December 2014, and nine dead in another attack in December 2017 in the same city.
Fazlullah was in charge of the Pakistan Taliban's (TTP) operations in the Swat Valley when activist Malala Yousafzai was shot in 2012.
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.
Three army soldiers were martyred and five militants killed in attacks from across the Pak-Afghan border on military posts in North Waziristan district on Friday, sources said. The Pakistani branch has been allied with several other terrorist groups, including the notorious Haqqani network, responsible for the deaths of many Americans in Afghanistan. Yousafzai was gravely wounded in a 2012 shooting after her advocacy as a youth for girls' education.
"We have been hearing since early Friday that our Emir (leader) was martyred along with four other militant commanders in Marawar area of Kunar".