The elusive Omar has not been seen in public since fleeing when the Taliban was toppled from power by a U.S.-led coalition in 2001, and there has been speculation for years among militant circles that he was either incapacitated or had died.
"We are aware of the reports of the passing of Mullah Omar, the Taliban leader," Sayed Zafar Hashemi, a spokesman for President Ashraf Ghani, told reporters.
"We are still in the process of verifying those reports, and as soon as we get any more accurate information or identification ... we will let the media and the people of Afghanistan know about it."
The comments came as preparations were under way for the next round of peace talks between Kabul and the Taliban, provisionally planned for Thursday or Friday in a location yet to be confirmed.
Read: Reclusive Taliban leader Mullah Omar died two or three years ago, say reports
Renewed uncertainty over Omar's fate could deepen divisions within the movement as rival commanders position to succeed him, in a possible setback for the fledgling peace process.
The Taliban is already split between senior figures who support talks with Kabul to end the 13-year war and others who want to continue to fight for power.
A senior Afghan Taliban commander based in neighbouring Pakistan said Omar had died of natural causes, although he did not specify when.
"We are at a crossroads, and it will take some time to resolve this (leadership) issue," the militant said.
He added that a group within the Taliban wanted one of Omar's sons to take over, while another favoured the promotion of political leader Akhtar Mohammad Mansour, who has been among those who support peace talks.
A written message purportedly from Omar released earlier in July indicated he also approved of dialogue, but there was no way of independently confirming that the document was genuine.
A senior official from the Pakistani military, which historically has close ties to the Afghan Taliban and other Islamist militant groups in the region, said he could not confirm Omar's death.
"It is worth asking why this news has come out now, when we are two days away from the second round of peace talks," said the official, who was not authorised to speak to the press.
"Especially in light of reports that he died two years ago ... why is this news being released now? It raises questions about the intentions of people who don't want talks to go forward."
Ghani is keen to broker a settlement with the insurgents, who have been gaining territory in pockets of the country and intensifying attacks on military and political targets.
Thousands of civilians and security personnel are killed each year in the violence, which has worsened since NATO withdrew most of its forces from the country at the end of last year.
