The monitoring group SITE quoted an Arabic language report on the terrorist group's Amaq propaganda agency as saying that three IS fighters had killed the two Russian policemen near the Dagestani city of Kizilyurt on Sunday.
Russia's National Anti-Terror Committee said in turn that, during an "anti-terror operation" in Dagestan on Sunday, police had neutralised "two bandits" involved in the killing of policemen.
The militants had a hunting rifle, a knife and a service gun belonging to one of the murdered policemen, the statement said without providing further details.
Islamist rebels from Dagestan, which lies immediately east of Chechnya, are known to have travelled to Syria to join IS.
In 2015, the Islamist group declared it had established a "franchise" in the North Caucasus.
It has claimed a number of attacks on police in Dagestan in the last couple of years that have involved guns and explosives, as local security forces battle a simmering Islamist insurgency.
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