Afghanistan's intelligence agency says the Afghan Taliban supreme leader, Mullah Omar, died two years ago in a Pakistani hospital.
Abdul Hassib Seddiqi said that Mullah Omar had died of health problems at a hospital in Pakistan.
Afghanistan's government says information on his death is "credible".
The latest reports of Mullah Omar's death are being taken more seriously than previous such reports.
The Taliban is expected to issue a statement today.
Sources at the Taliban's two main councils in Quetta and Peshawar in Pakistan told the BBC they were in intensive talks to agree on a replacement for Mullah Omar.
A statement from the office of Afghanistan's President Ashraf Ghani said that it believed, "based on credible information", that Mullah Omar died in April 2013 in Pakistan.
The Afghan government, elected last year, has embarked on a peace process with the Taliban.
In its statement, the government called on "all armed opposition groups to seize the opportunity and join the peace process".
A security official in Pakistan, the country hosting the talks, told AP that the claims of Mullah Omar's death were mere "speculation", designed to destabilise the negotiations.
Pakistan's government and security services have not formally commented on the claims so far. They have always denied that Mullah Omar was in their country.
The White House said it believed reports of his death were credible.
An elusive character
Mullah Omar had not been seen in public since the fall of the Taliban regime in late 2001.
The absence of confirmed contacts for several years fuelled speculation. His ill-health and even death have regularly been rumoured in the past.
Over the past two years, even some high-ranking Taliban started asking questions, both privately and within the Taliban circles, about their leader's health, life and ability to run the insurgency.
Despite his long absence from the public view, the mystique of the man has been overwhelming.
He had become a symbol and a unifying figure within the Taliban. While the day-to-day affairs have been managed by his deputies, everything else revolved around his name.
Questions about his life and whereabouts will only increase, putting pressure on the Taliban to produce credible evidence - if he is alive.