Abdulaev and two other Chechen fighters were reportedly killed on 18 January during a gunbattle in Agyshty, a small settlement in Chechnya's Shali region.
Chechen Interior Minister Ruslan Alkhanov said Abdulaev was among those responsible for propagating Wahhabism, a blanket word used in Russia to describe non-official Islam.
In a statement carried by the pro-independence news agency Daymokh, the Chechen separatist leadership says it is still unable to confirm Abdulaev's death.
(Interfax, ITAR-TASS, Daymokh)