Two districts in the southern Stavropol region were placed on high alert after the bodies were discovered in or close to parked cars, at least one of them apparently booby-trapped, in the rural area yesterday, the regional authorities said.
The Stavropol region borders the Krasnodar region where the Black Sea resort of Sochi is located.
"A counter-terrorism operation has been launched from midnight on January 9 in the Predgorny and Kirov districts of the Stavropol region," the regional administration said in a statement.
Three of the male victims have been identified, with one working as a taxi driver, it said.
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Russia particularly fears attacks by Islamist militants from the North Caucasus during the prestigious event, after two suicide bombings at a rail station and in a trolleybus last month in the southern city of Volgograd killed 34.
No one has claimed responsibility for that attack, but Russian media said the attackers came from the restive North Caucasus region of Dagestan.
As police examined one of the cars in Stavropol, which contained the body of a local resident who had been shot in the head, an improvised explosive device (IED) went off around 20 metres (65 feet) away, causing no injuries, the regional interior ministry said in a statement.
Officers then defused another device nearby, Interfax news agency cited the FSB security agency as saying.
A security source told Interfax the two devices were packed with small metal elements such as screws to cause maximum injury and resembled those previously used by insurgents in southern Russia.
The Investigative Committee, which probes major criminal cases in Russia, opened probes into murder, arms trafficking and attempts on the lives of law enforcement officials.
It said today that the series of murders, which took place within 24 hours, was to be treated as a single investigation.
A law enforcement source told Interfax that investigators were seeking three men from a village in the neighbouring Kabardino-Balkaria province.