The severe cold struck war-torn Ukraine at a time when thousands of both Russian and Ukrainian troops were engaged in intense fighting in the eastern towns near the Black Sea almost 22 months into Vladimir Putin's invasion.
Kyiv fears Moscow could attack its power grids with air strikes this winter.
In Ukraine, at least 10 people were killed and almost 1,500 towns and villages were left without power after storms dumped up to 10 inches of snow in some places.
“As a result of worsening weather conditions, 10 people died in Odesa, Kharkiv, Mykolaiv and Kyiv regions,” interior minister Ihor Klymenko said on Tuesday.
“Twenty-three people were injured, including two children,” he added.
The highest number of deaths were reported from the Odesa region, Ukrainian president Volodymyr Zelensky said in his nightly video address.
Schools were ordered to shut, while traffic was halted on 10 highways.
Southern Odesa, the Mykolaiv regions, and central Kyiv were the worst affected places, with initial power cuts reported in 40,000 homes in the capital region.
Ukraine is likely to be hit with more snow and rain on Tuesday, according to forecasters.
Nearly 2,500 people were rescued following a snowstorm in Odesa, local governor Oleh Kiper said. About 849 vehicles have been towed out, including 24 buses and 17 ambulances, he announced on Telegram, adding that all those trapped by the snow since the start of the snowstorm had now been rescued.
On Monday evening, the boiler facility in Odesa, where a 100-metre pipe broke and fell on Sunday, resumed operations.
The "storm of the century" killed at least four people in Russia and occupied Crimea after it struck the southern part of the country over the weekend.
Dagestan, Krasnodar and Rostov, as well as the occupied Ukrainian territories of Donetsk, Lugansk, Kherson, Zaporizhzhia and Crimea have been struggling with the violent weather conditions, the authorities said.
At least 1.9 million people were affected by power cuts in Russia, according to energy minister Nikolay Shulginov.
Huge waves crashed over beachside areas of the Black Sea coast, killing one person. One man, who "went out to look at the waves" died in the Russian-annexed Crimean peninsula, said Oleg Kryuchkov, an adviser to the region's Russian-installed governor.
Vladimir Konstantinov, a Crimean lawmaker, said the peninsula had experienced an "armageddon"-like scenario. "Old-timers can't remember this kind of wind and waves," he added.
In the resort cities of Sochi and Anapa, one person died and several people were injured when hundreds of trees were blown down.
In neighbouring Moldova, four people were reported dead during the cold snap that hit the region over the weekend. Two bodies were recovered from inside a car buried in a snowdrift in the southeastern area of Coscalia and another outside the capital.
Ukraine's border service said that two border crossings in the Odesa region to Moldova reopened after a temporary suspension on Sunday, but traffic conditions remained difficult.
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