Omar, the one-eyed, reclusive leader of the militant Islamists, is said to have vanished up to five days ago.
“We can confirm that he has disappeared from his hideout in Quetta, [capital of the southwestern Pakistani province] Baluchistan,” said Lutfullah Mashal, spokesman for the National Directorate of Security.
“So far we cannot confirm the killing of Mullah Omar officially.”
Mashal’s comments came hours after one Afghan intelligence source called a number of reporters to inform them, on condition of anonymity, that Omar had been killed in Pakistan by the Inter-Services Intelligence (ISI) agency.
Pakistani Interior Minister Rehman Malik said Pakistan had “no such information” on Omar’s alleged killing.
The Taliban denied that Omar is dead or missing.
Speaking by telephone from an undisclosed location, Afghan Taliban spokesman Zabihullah Mujahid said the claim was “pure propaganda”.
It was not immediately clear how Afghanistan would have such detail on Omar’s movements, although Mashal said the information came from “our sources and senior Taliban commanders”.
An Afghan source, speaking on condition of anonymity, said Omar had been killed on Friday, citing information received from sources within the Haqqani insurgent group, whose leaders are Pakistan-based.
The claim came three weeks after the killing of bin Laden by United States forces in Pakistan.
Omar created the world’s strictest Islamist state in Afghanistan in the 1990s, and sheltered Osama bin Laden and al-Qaida before the 2001 US-led invasion ousted the militants.
The Taliban were known for their strict enforcement of Sharia law, highly repressive attitude to women and bans on television and music.
In the insurgents’ 10-year war against foreign forces, Omar has continued to inspire fighters in Afghanistan. The US offers a reward of up to $10 million for bringing him to justice.