President Vladimir Putin inspected the damage by helicopter, the Kremlin said, amid recriminations from residents who accused authorities of abandoning them.
Television footage showed torrents of brown flood water gushing along streets in the worst-hit town of Krymsk past blanket-covered bodies. Residents were caught by surprise by the sheer force of the waters, which ripped up pavements and traffic lights and flooded buildings.
In Krymsk, some people woke in the middle of the night to find water pouring in, trapping them in their homes. One woman had to spend the night up a tree before being rescued.
Authorities estimated that up to 13,000 people had been affected in the Krymsk district. "Our house was flooded to the ceiling, we could not open the door because of the water, so we broke the window to climb out," Krymsk pensioner Lidiya Polinina told AFP by telephone.
"I put my five-year-old grandson on the roof of our submerged car, and then we somehow climbed up into the attic. I don't know how we managed to survive," she said, adding that they had received no warning or assistance.
Officials said at least 123 of the bodies had been recovered in the Krymsk area, including a 10-year-old child, but were unable to explain the scale of the toll there, saying the floods were caused by torrential rains.