"The leadership of the Caucasus Emirate officially announces the martyrdom of Emir Dokku Abu Usman," the Kavkaz Centre website said, using the Arabised nom-de-guerre of Umarov.
It gave no details of how he was said to have been killed and there was no confirmation from the Russian authorities who are usually keen to rapidly boast of the "liquidation" of top Caucasus militants.
"Foreign media periodically publish information about the liquidation of Doku Umarov but the Russian special services at this moment do not have such information and will not comment on it," the National Anti-Terror Committee said in a statement to the state RIA Novosti news agency.
The website also posted a video said to be of the bearded militant confirming the death of Umarov and outlining his leadership strategy for the Caucasus Emirate, which wants to impose an Islamic state across the mainly Muslim Northern Caucasus.
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Ali Abu Mukhammad was shown in battle fatigues at an undisclosed location with a gun behind him resting on a rock. He spoke in a mixture of Arabic and heavily-accented Russian. His origins and citizenship were not made clear.
"His soul is with the green birds in paradise," he added.
Ali Abu Mukhammad said he did not consider himself worthy of the duty but had taken it on after being asked "by the brothers".
"I will take on the responsibility myself," he said, saying the "jihad" by the Caucasus Emirate group would continue.