Ukraine says Russia has destroyed almost a third of its power stations over the past week as Moscow steps up a campaign to strike infrastructure, a move the West says is a calculated attempt to disrupt and demoralise.
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Missiles struck power generating facilities in a clutch of Ukrainian cities home to millions of people and several people were killed.
Moscow acknowledged targeting energy plants, while Ukraine said water infrastructure had also been hit.
"The situation is critical now across the country ... the whole country needs to prepare for electricity, water and heating outages," Kyrylo Tymoshenko, deputy head of the Ukrainian president's office, told Ukrainian television.
At least one man died when a Russian missile reduced his apartment in the southern river port of Mykolaiv to rubble.
Another two people were reported killed in a strike on Kyiv.
Ukrainian President Volodymyr Zelenskiy said Russia was continuing to try to terrorise and kill civilians.
"Since October 10, 30 per cent of Ukraine's power stations have been destroyed, causing massive blackouts across the country," he wrote on Twitter.
Power cuts were reported in parts of Kyiv, many parts of the Zhytomyr region west of the capital and Dnipro, which, like Mykolaiv, is in the south but also far from the front line where Ukraine is pressing Russian forces occupying its southeast.
Zelenskiy reiterated his refusal to negotiate with Russian President Vladimir Putin whom he has accused of immorality.
"The terrorist state will not change anything for itself with such actions," he wrote on the Telegram messaging app. "It will only confirm its destructive and murderous essence, for which it will certainly be held to account."
Putin has dismissed Zelenskiy as a puppet of Washington, which has given Kyiv more than $US17.5 billion in security aid.
There was no immediate word on how many people had been killed in Tuesday's strikes overall, which came a day after Russia sent swarms of drones to attack infrastructure in Kyiv and other cities, killing at least five people.
The Russian defence ministry, whose troops have this month been forced to retreat on two separate fronts, reiterated that it was carrying out attacks on military targets and energy infrastructure across Ukraine with high-precision weapons.
Russia earlier this month named General Sergei Surovikin as overall commander of Moscow's forces in Ukraine. Surovikin served in Syria and Chechnya where Russian forces pounded cities to rubble in a brutal but effective scorched earth policy against its foes.
Nicknamed "General Armageddon" by the Russian media because of his alleged toughness, his appointment was followed by the biggest wave of missile strikes against Ukraine since Moscow invaded on February 24.
Putin cast those strikes as revenge for what he said was a Ukrainian attack on the bridge which links Russia to Crimea - the peninsula Russia annexed from Ukraine in 2014. At least three people were killed in the bombing for which Ukraine has not officially taken responsibility.
In Mykolaiv, a strategic port which Russia tried and failed to capture earlier in the war, a Reuters witness said they had heard three explosions in the early hours of Tuesday.
A missile had completely destroyed one wing of a building in the downtown area, leaving a massive crater, they said. A fire crew was seen pulling the dead body of a man from the rubble.
The governors of Russia's Kursk and Belgorod regions, which border Ukraine, on Tuesday reported cross-border shelling.
In Belgorod, a train station was shelled and train links suspended, and two villages were shelled in Kursk, leading to electricity outages, they said.
Australian Associated Press
