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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Image Galleries: Russia in World War I
Infographics: World War I, 1914-1918
The self-defense forces in Donbass likely do not have the capability to win. Kiev will simply outlast the republic’s fighters. Ukraine still has many mobilization resources. The most important thing for self-defense fighters is not to win the war but rather not to lose it.