"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 Shiite 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.
"Four of the Russian soldiers were killed in Qasr al-Halabat west of Palmyra during an attempt to storm the area that IS forces foiled, while the advisor whose corpse was shown in a video distributed by the agency died (Thursday) in the Dawa area," Aamaq claimed.
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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, sending shock waves across the world.
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.
The Russian air force has however continued to strike jihadist targets since the surprise announcement, particularly around Palmyra.
Russia's defence ministry did not reply to an AFP request for information on the jihadist claim.
"Our uncompromising attitude to terrorism remains unchanged," Putin said Thursday, adding that "fierce fighting" was raging near Palmyra.
He also named four Russians killed in action in Syria since Moscow launched a military intervention in Syria on September 30, including a military advisor.
Previously, the defence ministry's official toll had been three, excluding a soldier who committed suicide.