Flash floods affected parts of the Krasnodar region, including the area around the Black Sea resort city of Sochi, where Moscow hosted the Winter Olympics in 2014.
Russia's emergencies ministry said it had recovered the bodies of six people while clearing rubble. Two people were hospitalised.
Officials opened investigations into the deaths of an 81-year-old man and a 71-year-old woman who drowned separately in their homes.
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Another 67-year-old woman was missing after strong currents sucked her into a ditch and carried her away, the Investigative Committee said.
Kremlin spokesperson Dmitry Peskov told journalists all government services were "working in emergency mode" to battle the "ruthless elements."
The emergencies ministry said more than 2,300 houses were flooded in the region.
Flash floods frequently cause devastation in the area wedged between the Black Sea and the Caucasus mountain range as mountain rivers swell and destroy settlements below.
Similar floods in 2012 killed more than 150 people around Krymsk, another town in the region.
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A regional subsidiary of Russian oil transport company Transneft said Friday that the flash floods and resulting landslides "damaged a pipeline" in the region's Tuapse district causing "a spill of five cubic metres of oil."
The company was working to keep the oil from getting into the Tuapse river, a major source of water for the town of Tuapse, home to more than 60,000 people.
The floods also damaged a major railway line and roads, authorities said. Russian Railways, the country's rail monopoly, said 31 passenger trains were stopped due to the damage, and passengers were being bussed to the nearest stations to continue their journeys.
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