Russia's national anti-terrorism committee said yesterday in a statement quoted by TASS news agency that 11 "bandits" were killed in a first raid near the city of Nalchik. Three others died in a second operation in the same area later in the day.
"All of them were participants in an armed gang whose members swore loyalty to IS," it said.
The fighters opened fire on law enforcement officers and threw grenades after they were cornered in a wooded area outside Nalchik in the Kabardino-Balkaria region, the anti-terrorism committee said.
A police source told Interfax news agency that the new leader of a local IS cell and two deputies were among those killed, and that a "large cache" of munitions was seized.
Islamists in the North Caucasus have previously been united under a local Caucasus Emirate organisation, but are now increasingly flocking to Islamic State, which in June declared it had established a franchise there.
Earlier this month, Russia said it had killed the supposed head of an IS-linked gang in Kabardino-Balkaria, saying he had vowed allegiance to IS and organised the murders of several officials, gunning down one in front of his son.
Kabardino-Balkaria is usually seen as one of the more peaceful parts of Russia's North Caucasus.
Moscow is conducting intensive air strikes targeting IS infrastructure in Syria and has been pushing for the creation of an international anti-IS coalition, which would include Russia, the West and some Middle Eastern states.
The jihadist group claimed responsibility for the bombing of a Russian passenger jet last month that killed all 224 people on board, prompting Russia to step up its strikes against the group.
President Vladimir Putin has estimated that there are between 5,000 and 7,000 people from former Soviet countries fighting with IS.