If confirmed, the killing of Russian soldiers would come just days after announcement from Moscow of partial pull out from the country
The Islamic State militant group has claimed the killing of five Russian troops in fighting near the ancient Syrian city of Palmyra.
"The soldiers of the caliphate, by the grace of God, have killed five Russian soldiers and six members" of the Syrian army, IS said in a statement.
The group also claimed the killing of several members of the Lebanese Shia Hezbollah group in fighting near Palmyra.
A website linked to IS, Aamaq, carried a similar claim, adding that one of the Russians killed was a military advisor.
Aamaq said that four soldiers were killed in Qasr al-Halabat, west of Palmyra, while attempting to storm an area.
A Russian advisor, the website reported, was killed in the nearby Dawa area. Aamaq published a video, showing the bloodied corpse of a man in military gear that it claimed was the advisor.
The footage also shows equipment presumably captured, including a customised AK-74M rifle, a helmet and a compass. A packet of bandages was filmed with instructions written in Russian.
IS seized Palmyra, a UNESCO World Heritage Site in eastern Syria known as the "Pearl of the Desert", last May.
The Syrian Observatory for Human Rights monitor said that Russian advisors were present near Palmyra, but could not confirm whether any Russian forces had been killed there in recent days.
President Vladimir Putin, one of Assad's main backers along with Iran, on Monday ordered the withdrawal of most of Russia's armed forces from Syria.
The Russian air force has however continued to strike militant targets since the surprise announcement, particularly around Palmyra.
Russia's defence ministry did not reply to an AFP request for information on the militant claim.
"Our uncompromising attitude to terrorism remains unchanged," Putin said on Thursday, adding that "fierce fighting" was raging near Palmyra.
He also announced that Russia's defence ministry has spent $484mn on its military operations in Syria so far.
In his remarks, Putin named four Russians killed in action in Syria since Moscow launched a military intervention in Syria on 30 September, including a military advisor.
Previously, the defence ministry's official toll had been three, excluding a soldier who committed suicide.