Rustam Gelayev, son of Ruslan Gelayev, "entered into a battle with superior forces of the Alawite regime in a Syrian district, presumably between August 11 and August 13," the KavkazCenter website said.
"During the fighting, he was martyred," said the website, which is regularly used by Russian-based Islamic militants to exchange information and has developed a history of providing accurate battlefield reports.
The elder Gelayev was one of the top commanders in Chechnya's first war for independence that killed tens of thousands between 1994 and 1996 and ended with the region winning broader sovereignty within Russia.
The elder Gelayev joined the second war as well, which continued to simmer for years after Russian troops claimed control over Chechnya's main cities in 2000. He was killed in 2004 while leading a group of gunmen in battle against Russian border guards in the neighbouring North Caucasus region of Dagestan.
KavkazCenter said the younger Gelayev was born in 1988 and had lived for a most of his life in Russia before receiving an Islamic education in an unnamed Middle East country. He came to Syria in the summer, said the website, citing unnamed sources and members of the Chechen diaspora in Europe.