The gunmen opened fire from a Lada car after police had stopped the vehicle.
"The militants were killed as the police returned fire," the source said.
No police officers were injured in the shootout. Two Kalashnikov assault rifles, a Makarov pistol, and a hand grenade were found in the car.
Russia's volatile North Caucasus region has seen a surge in militant attacks against police and civilians in recent months.
In a separate development, an explosive device containing 5.5 kg of TNT and filled with nuts and bolts to increase its destructive power was found in the village of Neitrino in the republic's Elbrus Region.
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Any response would likely boomerang on Russia – the partnership between Rosneft and ExxonMobil is a case in point. The United States has hit Russia with a third round of sanctions. This time the Americans went with a higher caliber weapon, targeting Russia’s biggest energy companies (Rosneft and Novatek) and banks (VEB and Gazprombank).