Haqqani network was held responsible for attacks including the Indian embassy bombing and the attack on Kabul Serena Hotel in 2008, and the 2009 coordinated attacks on the Afghan justice ministry.
Some Pakistani media reported death of Jalaluddin Haqqani, the founder of Haqqani network, an allied group of Taliban, Dawn online reported.
The report came when his son Sirajuddin was announced as one of the deputy chiefs of the Taliban following the death of Mullah Omar.
"Some media outlets spread reports... about the death of a distinguished jihadi personality... Jalaluddin Haqqani," the Taliban said in a statement posted on their website.
"This claim has no basis. Haqqani... was ill before but he has been blessed with good health for a prolonged period now and has no troubles currently."
The rumour of Jalaluddin's death has also been rejected by his family, said a an Afghan Taliban commander.
"I talked to his grandson (who is somewhere in eastern Afghanistan) and he completely rejected rumours of his death," the commander said.
"My grandfather is alive, I talked to him last week. He was weak and sick but alive and in good spirits', he told me."
The Afghan Taliban named Mullah Akhtar Mansour as their new chief on Friday. The Taliban also announced his deputies - Sirajuddin, who has a $10 million US bounty on his head, and Haibatullah Akhundzada, former head of the Taliban courts.
Haqqani network is militarily the most capable and most dangerous of the Taliban factions.
The group is present both in its stronghold in eastern Afghanistan and in the tribal districts of North Waziristan in Pakistan's restive northwest along the Afghan border.