The operation began Wednesday in the Stavropol Territory after a vehicle exploded with a person inside as police approached it, RIA Novosti reported.
Police later discovered two bodies in two other vehicles in the same region Wednesday, along with two more bodies and explosive materials in a car Thursday, the newspaper said.
Police said they believe all were victims of homicide.
Police began counter-terrorism operations in the Kirovsky and Predgorny districts in response to the deaths and explosion, ITAR-Tass reported.
"In view of a possible terrorist threat, interaction has been arranged between the operations headquarters and operations headquarters in the constituent entities of the North Caucasus and Southern Federal Districts," a source with the operation said.
The Stavropol Territory is about 500 miles from Sochi, where the 2014 Winter Olympics are scheduled to begin Feb. 7.