with a $25 million bounty on his head is known for his strict adherence to Sharia law and hard line on women's rights.
He is said to have vanished up to five days ago.
"We can confirm that he disappeared from his hideout in Quetta, (the capital of the southwestern Pakistani province) Baluchistan," said Mashal, spokesman for the National Directorate of Security (NDS).
"He disappeared from his location during the last four to five days," he added, speaking in English. "So far we cannot confirm the killing of Mullah Omar officially."
Mashal's comments came hours after one Afghan intelligence source called a handful of reporters to tell them, on condition of anonymity, that Omar had been killed in Pakistan by the Inter Services Intelligence (ISI) agency.
A separate source later told AFP that he had been missing for 11 days.
The Taliban have denied that he is dead or missing.
Speaking to AFP by telephone from an undisclosed location, Afghan Taliban spokesman Zabihullah Mujahid said the claim was "pure propaganda". His Pakistani counterpart Ehsanullah Ehsan said the news "has been spread to weaken the Taliban."
The claim came exactly three weeks after the killing of al Qaeda leader Osama bin Laden by US Navy SEALs in Pakistan.
It was not immediately clear exactly how Afghanistan would have such detail on Omar's movements, although Mashal said the information came from "our sources and senior Taliban commanders."
The first Afghan source, speaking on condition of anonymity, said that Omar had been killed on Friday, citing information received from sources within the Haqqani insurgent group, whose leaders are based in Pakistan.
"Based on ISI instruction" through former ISI chief Hamid Gul, Mullah Mohammad Omar was told to move from Quetta to the tribal district of North Waziristan, which borders Afghanistan, the source said.
"As Mullah Omar was being transported from Quetta to North Waziristan by the ISI, he was secretly killed by the ISI."
However, a second Afghan intelligence source who also spoke anonymously said that Omar had been missing for 11 days following a meeting with Gul. "It has been 11 days since his close circle, the people around him, have no clue of his whereabouts. The Taliban leadership are all concerned and worried for the sudden disappearance of Mullah Omar," the source said.
Gul described the claims by the sources as "totally false".
"I never met Mullah Omar, not even once in my life," he told AFP.
"This has been fed by the Indian lobby to defame Pakistan and me. I don't think he is in Pakistan. He never came into Pakistan, even during the Soviet Union war (in Afghanistan)."
Pakistani interior minister Rehman Malik also told media that Pakistan had "no such information" on Omar's alleged killing.
"There has been no report available to us about any operation that has happened in Pakistan. If Mullah Omar has been killed in Afghanistan, it is up to the Afghan authorities to confirm or deny," he said.
Afghanistan and Pakistan regularly trade accusations over Taliban insurgencies plaguing both their countries. There is deep distrust between Afghan intelligence and the ISI, which helped create the Taliban in the 1990s.
Omar created the world's strictest Islamist state in Afghanistan in the 1990s, and sheltered Osama bin Laden and al Qaeda 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 United States offers a reward of up to $10 million for bringing him to justice.