Ukraine and Russia blamed each other for the collapse of the massive dam on Tuesday, which sent floodwaters across a swathe of the war zone and forced thousands to flee.
Ukraine said Russia committed a deliberate war crime in blowing up the Soviet-era Nova Kakhovka dam, which powered a hydroelectric station.
The Kremlin blamed Ukraine, saying it was trying to distract from the launch of a major counteroffensive Moscow says is faltering.
UN aid chief Martin Griffiths told the Security Council the dam breach "will have grave and far-reaching consequences for thousands of people in southern Ukraine on both sides of the front line through the loss of homes, food, safe water and livelihoods".
"The sheer magnitude of the catastrophe will only become fully realised in the coming days," he said.
No deaths were initially reported, but US spokesman John Kirby said the flooding had probably caused "many deaths".
Ukrainian officials estimated about 42,000 people were at risk from the flooding, which is expected to peak on Wednesday.
In Kherson city, about 60km downstream from the dam, water levels rose by 3.5 metres on Tuesday, forcing residents to slog through water up to their knees to evacuate, carrying plastic bags full of possessions and small pets in carriers.
"Everything is submerged in water, all the furniture, the fridge, food, all flowers, everything is floating," Oskana, 53, said when asked about her house.
"I do not know what to do."
Buses, trains and private vehicles were marshalled to carry people to safety in about 80 communities threatened by flooding.
In Kherson, cracks of incoming artillery sent people trying to flee running for cover on Tuesday.
In the evening, Reuters reporters heard four incoming artillery blasts near a residential neighbourhood where civilians were evacuating.
Residents in flooded Nova Kakhovka on the Russian-controlled bank of the Dnipro told Reuters some had decided to stay despite being ordered out.
"They say they are ready to shoot without warning," said one man, Hlib, describing encounters with Russian troops.
The Kazkova Dibrova Zoo on the Russian-held riverbank was completely flooded and all 300 animals were dead, a representative said via the zoo's Facebook account.
"More and more water is coming every hour," Yevheniya, a woman in Nova Kakhovka, said by telephone.
"It's very dirty."
Washington said it was uncertain who was responsible, but Deputy US Ambassador to the UN Robert Wood told reporters it would not make sense for Ukraine to destroy the dam and harm its own people.
The Geneva Conventions ban targeting dams in war because of the danger to civilians.
Ukrainian President Volodymyr Zelenskiy said in a video address his prosecutors had already approached the International Criminal Court about the dam.
Earlier, he claimed on Telegram that Russian forces blew up the power plant from inside.
"Residents are sitting on the roofs of their homes waiting to be rescued," Oleksiy Kuleba, a senior official on Zelenskiy's staff, said on Telegram.
"This is a Russian crime against people, nature and life itself."
The dam supplies water to a wide area of southern Ukrainian farmland, including the Russian-occupied Crimean peninsula, as well as cooling the Russian-held Zaporizhzhia nuclear plant.
The UN nuclear watchdog said Zaporizhzhia, upriver on the reservoir, should have enough water to cool its reactors for "some months" from a separate pond.
As Kyiv prepares for a long-awaited counteroffensive, some military analysts said the flooding could benefit Russia by slowing or limiting any potential Ukrainian advance along that part of the front line.
