Afghanistan on Wednesday said Omar died two years ago in Pakistan, in the first such official confirmation from Kabul after unnamed government and militant sources reported the demise of the reclusive warrior.
The insurgents have not officially confirmed his death, and the claim -- just two days before a fresh round of talks were expected -- cast doubt over the tenuous peace process.
"Media outlets are circulating reports that peace talks will take place very soon... either in the country of China or Pakistan," the Taliban said in an English-language statement posted on their website on Thursday.
"(Our) political office... are not aware of any such process," added the statement, which prompted no immediate reaction from the Afghan government.
The statement marked the first comment from the group, which has waged an almost 14-year insurgency against Afghan and foreign forces, since Kabul's dramatic announcement on Wednesday citing "credible information".
Mullah Omar has not been seen publicly since the 2001 US-led invasion of Afghanistan that toppled the Taliban government in Kabul.
Haseeb Sediqi, the spokesman for Afghanistan's National Directorate of Security, told AFP that Omar died in hospital in the Pakistani city of Karachi "under mysterious circumstances".
Rumours of Omar's ill-health and even death have regularly surfaced in the past, but the White House added weight to Kabul's latest assertion, calling reports of his demise "credible".