The militants were shot Sunday when police in the southern republic of Kabardino-Balkaria stopped a vehicle to check the occupants' documents, RIA Novosti said Monday.
People in the vehicle began shooting, police said in a statement. The alleged militants were killed in return fire.
"According to our information, the militants were preparing to stage terrorist attacks in churches of Kabardino-Balkaria and the Stavropol Territory during Christmas divine services," the statement said.
No police officers were injured, a source told ITAR-Tass.
During the gunfire, the vehicle exploded and caught fire, burning those inside and hindering their identification, the source said.
An automatic rifle, two handguns and ammunition were found at the scene.