The Taliban leadership said it was investigating what it called “claims” that Ayman al-Zawahri was killed in the strike on Sunday, and warned the US not to repeat drone strikes on Afghan soil.
The group said in a statement that "if such incidents are repeated again and if the territory of Afghanistan is violated then responsibility for any consequences will be on United States."
It insisted that it had “no knowledge of the arrival and residence" of al-Zawahri in Afghanistan.
However, US officials have said the al-Qaeda head was staying at a Kabul safe house linked to the deputy leader of the Taliban.
The strike killed al-Zawahri when he stepped out onto the safe house’s balcony.
“The government and the leadership wasn’t aware of what is being claimed, nor any trace there,” the Taliban insisted in a statement.
“Investigation is underway now to find out about the veracity of the claim”.
The Taliban had promised in the Doha Agreement not to harbour al-Qaeda members or those seeking to attack the US.
In the accord, the US committed to withdraw its troops from Afghanistan and not to attack the Taliban.
The Taliban claimed the drone strike was a breach of the agreement.
Relations between Afghanistan and the US have become strained after al-Zawahri was discovered there.
The Taliban has appeared to try and defuse tensions as it seeks an urgent infusion of cash to handle the catastrophic collapse of the economy that came after the US withdrawal a year ago.
The Taliban said they ordered "the investigative and intelligence agencies to conduct serious and comprehensive investigations on various aspects of the mentioned event."
The statement also assured the West "there is no danger from the territory of Afghanistan to any country, including America."
Pakistan, which has lobbied the world to improve ties with the Taliban, said Thursday that its airspace was not used for the strike that killed al-Zawahri.
US officials have not confirmed from where the drone with precision-guided Hellfire missiles was launched.