Doku Umarov, who styles himself the "Caucasus Emir", was killed in a security operation, Kadyrov said in a statement published Friday on the Chechen government's website.
"We are 99.9 per cent sure of this," Kadyrov said.
"I said before that he was no longer alive, but now we have received a recording of a conversation of so-called 'emirs' where they announce his death, condole with each other and discuss candidates to replace him as emir."
"We cannot confirm the death of Doku Umarov. We do not have any such information," a source in Russian security services told the Interfax news agency.
More From This Section
Lawmaker and former security agency chief Nikolai Kovalyov told RIA Novosti news agency that rebels often spread false information of deaths in order to evade pursuit.
"I am sure the Chechen president has reliable information in order to make such claims. He has evidence of his death. But of course this information must be double-checked," he added.
Umarov vowed in July that his fighters would use "any means possible" to keep Putin from staging the Games.
Russia has enforced drastic security measures in and around the host city Sochi in a bid to prevent major attacks by insurgents after bombings in the southern city of Volgograd last month killed 34.