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Several people have been killed after Russia launched its largest aerial attack on Ukraine since August.
More than 200 missiles and drones were deployed, Volodymyr Zelenskyy said, as he condemned a "massive combined strike" on "all regions".
Andrii Sybiha, Ukraine's foreign minister, said "peaceful cities" and "sleeping civilians" were targeted.
Moscow is focused on the "energy infrastructure throughout Ukraine" and is trying to intimidate Ukrainians with "cold and lack of light", Mr Zelenskyy said.
The president added: "The whole world sees and knows that we are defending ourselves against absolute evil, which does not understand any language but force.
"We need unity [and] the world needs unity. Only together can we stop this evil."
Two people were killed and a 17-year-old boy was injured after a Russian attack in the Black Sea port of Odesa, regional governor Oleh Kiper said.
Energy infrastructure was damaged, he said, leading to "interruptions in the supply of heat, water and electricity".
In Mykolaiv, southern Ukraine, officials said two people were killed in a Russian drone attack.
Ukraine's state emergency service said a multi-storey building, cars and a shopping centre were hit.
Two women were killed and six injured, including two children, it added.
In the central Dnipro region, two people died and three were wounded in a strike on a rail depot, while in Lviv, on the border with Poland, a woman was killed in a car.
In the capital, Kyiv, mayor Vitali Klitschko said Russian attacks had caused a fire to erupt on the roof of a residential building, injuring at least two people.
People took refuge in metro stations, while emergency services were pictured removing part of a Russian missile from an apartment block.
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The Ukrainian military said it had destroyed 102 missiles and 42 drones launched by Russia.
Hypersonic missiles were among the 120 fired at Ukrainian territory, it said.
Air defences were active in "almost all" regions of Ukraine.
Equipment at thermal power stations has been "seriously damaged" during Russian air strikes, Ukraine's largest private energy provider said. DTEK said its staff were working on repairs.
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Russia's defence ministry confirmed it had attacked energy resources supporting Ukraine's military-industrial complex, Russian news agencies reported.
Poland scrambled its air force early on Sunday because of the "massive attack by the Russian Federation using cruise missiles, ballistic missiles and unmanned aerial vehicles".
Mr Zelenskyy sent his condolences to anyone affected by the latest Russian attacks.
He said "all necessary forces" were involved in restoring power and facilities.
On Tuesday, it will be 1,000 days since Russia launched what it calls its "special military operation".
English (US) ·