Residents slogged through flooded streets carrying children on their shoulders, dogs in their arms and belongings in plastic bags while rescuers used rubber boats to search areas where the waters reached above head height.
Ukraine said the deluge would leave hundreds of thousands of people without access to drinking water, swamp tens of thousands of hectares of agricultural land and turn at least 500,000 hectares deprived of irrigation into "deserts".
Visiting the city of Kherson downstream from the dam, Deputy Prime Minister Oleksandr Kubrakov said more than 80 settlements had been affected by the disaster and that the flooding had loosened chemicals and infectious bacteria into the water.
The Nova Kakhovka dam collapse on Tuesday coincides with a looming, long-vaunted Ukrainian counteroffensive against Russia's invasion.
Both sides traded blame for continued shelling across the populated flood zone and warned of drifting landmines unearthed by the flooding.
"Water is disturbing mines that were laid earlier, causing them to explode," Kubrakov said.
Ukraine said on Wednesday its troops in the east had advanced by more than a kilometre around the ruined city of Bakhmut in eastern Ukraine, its most explicit claim of progress since Russia reported the start of the Ukrainian counteroffensive earlier this week.
Russia said it had fought off the assault.
Oleksiy Danilov, secretary of Ukraine's national security council, said assaults underway were still localised, and the full-scale offensive had yet to begin.
"When we start (it), everyone will know about it, they will see it," he told Reuters.
Ukraine said several months ago the dam had been mined by Russian forces that captured it early in their 15-month-old invasion, and has suggested Russia blew it up to try to prevent Ukrainian forces crossing the Dnipro in their counteroffensive.
Ukrainian President Volodymyr Zelenskiy called the destruction of the Soviet-era dam "an environmental bomb of mass destruction" and a war crime, saying Russia had blown up the complex's power plant from within.
Russian President Vladimir Putin accused Ukraine of destroying the dam at the suggestion of its allies, saying it was a "barbaric" war crime that escalated the conflict with Russia.
Putin described the incident as an "environmental and humanitarian catastrophe," according to a Kremlin read-out.
Neither side has presented public evidence demonstrating who was responsible.
Some experts say the dam may have collapsed due to earlier war damage and poor Russian management.
Turkish President Tayyip Erdogan has proposed a commission of inquiry to look into the destruction of the dam.
Erdogan raised the issue in separate telephone conversations with Putin and Zelenskiy on Wednesday, the presidential office in Ankara announced.
Russia imposed a state of emergency in the areas of Kherson province it controls, where many towns and villages lie in exposed lowlands below the dam.
In the town of Nova Kakhovka right next to the dam, brown water submerged main streets largely empty of residents.
More than 30,000 cubic metres of water were gushing out of the dam's reservoir every second and the town was at risk of contamination from the torrent, Russia's TASS news agency quoted the Russian-installed mayor, Vladimir Leontyev, as saying.
Zelenskiy also said he was "shocked" at what he called the lack of United Nations and Red Cross aid so far for victims of the disaster, and Prime Minister Denys Shmyhal urged international humanitarian organisations to step up urgently.
Shortly afterward, President Emmanuel Macron of France said on Twitter that "within the next few hours we will send aid to meet immediate needs".
The UN's humanitarian affairs office said a team was in Kherson to co-ordinate relief efforts.
Access to drinking water was a major concern and about 12,000 bottles of water and 10,000 purification tablets had been distributed so far.
with DPA
