A text message was recently sent to journalists saying Omar was dead.
On Wednesday, a Taliban spokesperson said the group's phones and websites were hacked and the message is fake.
This is not the first time speculation of Omar's death has surfaced. In May, the Taliban also denied reports its leader was dead.
Omar has led the decade-long insurgency against the U.S.-led military coalition and the Afghan government of President Hamid Karzai. He ruled most of Afghanistan as leader of its Taliban government before the United States and its allies invaded on Oct. 7, 2001, in the wake of the Sept. 11 attacks.
Meantime, NATO says it has no knowledge of Omar's condition or whereabouts.
The Associated Press contributed to this report.