It was the second attack in Russia in 10 days claimed by IS after a man armed with an axe wounded seven in the Siberian city of Surgut on August 19.
Russian investigators have said they are investigating both attacks as criminal incidents, despite the claims by IS.
The attackers used knives to stab the two police officers before being "eliminated" at a petrol station in the Caspian Sea town of Kaspiisk, the regional Investigative Committee said.
The claim came after a reporter on Rossiya 24 television quoted law enforcement sources as saying that one of the attackers had a black jihadist banner in his rucksack.
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The reporter said it appeared to be "an attempt to repeat" recent stabbings in western Europe claimed by the jihadist group.
An unidentified source also told the state TASS news agency that investigators found two knives and items with the IS logo.
Islamist rebels from Dagestan, which lies immediately east of Chechnya, are known to have travelled to join IS. In 2015, the group declared it had established a "franchise" in the North Caucasus.