The statement on the Kavkaz Center site, which has not been confirmed, is the first time Umarov has been declared dead by his allies, CNN said. The Chechen government has reported Umarov, one of the most wanted men in Russia, dead in the past.
The website gave no details about where or how Umarov died, describing him only as a "martyr."
The website said that Ali Abu Mohammed has assumed leadership of the Caucasus Emirate, a group founded in 2007 to unite Chechen militants fighting for an Islamic state in Chechnya. Umarov threatened violent attacks at the recent Winter Olympics in Sochi and said his group was responsible for a 2011 bombing at the Moscow Airport.