Forecasters say more snow and rain is expected across the country on Tuesday.
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At least 10 people have died and 23 others have been injured in winter storms that have lashed central and southern Ukraine since the weekend.
The country's Ministry of Energy said more than 2,000 towns and villages were without electricity in 16 areas, including the Kyiv, Odesa, Mykolaiv, and Kirovohrad regions.
With the extreme weather creating treacherous conditions on roads across the country, some 1,530 vehicles have had to be towed away from snow drifts.
Ukrainian authorities shared images of damaged power grid facilities, toppled trees, flooding, and rescuers helping people on snow-covered roads.
The situation has piled extra pressure on emergency services and an energy grid that is already burdened by Russia's invasion.
In his nightly address on Monday, President Volodymyr Zelenskyy thanked rescue workers and volunteers, adding that engineers were working hard to restore power to communities.
“It is important to do everything possible to avoid casualties due to bad weather. Unfortunately, as of now, there are casualties. My condolences to the families and friends,” he said.
In illegally annexed Crimea, the Russian-installed authorities have declared a state of emergency in 10 municipalities following damage caused by the storm which has left more than 100,000 people without electricity.
Forecasters said more bad weather was on the way, with snow and rain forecast across the country on Tuesday.