Residents in Krasnodar say authorities failed to warn them in the lead-up to the worst natural disaster in the area in a decade.
More than 170 people are now confirmed dead after heavy rains caused flash floods in southern Russia.
Russian President Vladimir Putin has ordered investigators to find out if enough was done to prevent so many people being killed in floods in southern Russia, after flying to the region to deal with the first big disaster of his new presidency.
The investigations will determine whether city authorities could have done more. And whether the opening of sluice gates at a nearby reservoir could have caused the floods.
On Sunday, local officials admitted there had been a series of controlled releases as the rain fell on Friday night.
Torrential rains dropped up to a foot of water in less than 24 hours, which the state meteorological service said was five times the monthly average.
Putin personally inspected the damage late on Saturday, telling local officials that a top investigator would conduct a probe to see "who acted how".
"I asked the head of Russia's Investigative Committee to come here. He will check the actions of all the officials: when did the warning come, how did it come, when it could have come, when it should have come, and who did what."
Putin added he'd been told the reservoir was not technically able to disgorge such a volume of water.
Most of the victims died in or around Krymsk, a town about 300km northwest of Sochi, the Black Sea resort where Russia will host the 2014 Winter Olympics, with another 13,000 affected in the Krasnodar region.
Many of the dead were elderly people who had been sleeping and drowned.
The rising waters came when a torrential downpour on Friday night brought a month's worth of rain to the Krasnodar region in just a few hours.
"Everything happened at night and very quickly," the regional administration said in a statement.
Authorities said they had to switch off power in the worst-affected areas, including the district of Krymsk, to avoid more deaths after reports of residents in Gelendzhik dying of electrocution.
Putin, who was criticised for his slow reaction to disasters earlier in his career, also ordered money to be put aside for building new homes for victims in Krasnodar, a relatively rich area with thriving agriculture and tourism industries.
Novorossiysk, the nation's largest Black Sea port, which had received two months' worth of rain in a 24-hour period, has suspended exports of grain, metals and crude oil.
A team at the port had worked through the night to bring the situation under control, port spokesman Mikhail Sidorov said.
"In some places the water level reached 1.5 metres," he told AFP.
The floods and a landslide had affected the port's operations, and pipeline operator Transneft had informed management that it would halt shipments of crude oil, he added.
A Kremlin statement said Putin is "regularly receiving information about the state of affairs in Kuban from the health, emergencies situations and regional development".
Alexander Tkachev, Krasnodar's governor, said he had spoken by telephone to both the president and Dmitry Medvedev, the prime minister, and pledged everything would be done to help those affected by the floods.
The State Hydrometeorology Agency said more rain was possible on Saturday and Sunday, as Tkachov urged people not to panic.