The official, who said there had been lengthy leadership discussions for two days, declined to be identified. He did not confirm that Zawahiri was in the house that the missile struck.
How the Taliban react could have significant repercussions as the group seeks international legitimacy, and access to billions of dollars in frozen funds, following their defeat of a U.S.-backed government a year ago.
Zawahiri, an Egyptian doctor, was closely involved in the Sept. 11, 2001, attacks on the United States and was one of the world's most wanted men.
His death in Kabul raises questions about whether he received sanctuary from the Taliban, who had assured the United States as part of a 2020 agreement on the withdrawal of U.S.-led forces that they would not harbour other militant groups.
U.S. Secretary of State Antony Blinken said the Taliban had "grossly violated" the agreement by hosting and sheltering Zawahiri.
Outside a tight circle of top Taliban leaders, group members appeared in the dark about whether Zawahiri was actually in Kabul, let alone his fate.
Another Taliban official confirmed the high-level meetings but said he did not know what was being discussed and he did not believe Zawahiri was in the house.
Suhail Shaheen, the designated Taliban representative to the United Nations, who is based in Doha, told journalists he had received no word on the Taliban position.
"I am awaiting details and reaction from Kabul," he told reporters in a message.