Russia launched a wave of missiles at Ukraine on Thursday, a day after Germany and the US pledged tanks to aid Kyiv's fight against the invasion.
One person died and two others were injured after strikes hit a building in Kyiv, the city's mayor said.
Officials also reported strikes on two energy facilities in the southern region of Odesa.
The barrage came as Russia said it perceived the tank offer as "direct" Western involvement in the conflict.
In what was a sustained and wide-ranging attack, the head of the Ukrainian army said Moscow launched 55 air and sea-based missiles on Thursday.
Valery Zaluzhny added that 47 of them were shot down, including 20 around Kyiv.
Earlier, Ukraine's air force said it had downed a cluster of Iranian-made attack drones launched by Russian forces from the Sea of Azov in the south of the country.
A 55-year-old man was killed and two others wounded when non-residential buildings in the south of the capital were struck, officials reported.
The offensive was a continuation of Russia's months-long tactic of targeting Ukraine's infrastructure. The freezing winter has seen power stations destroyed and millions plunged into darkness.
After Thursday's strikes, emergency power cuts were enforced in Kyiv and several other regions to relieve pressure on the electricity grid, said DTEK, Ukraine's largest private power producer.
A day earlier, German Chancellor Olaf Scholz promised to provide Ukraine with 14 Leopard 2 tanks, following weeks of international pressure. They are widely seen as some of the most effective battle tanks available.
The heavy weaponry is expected to arrive in late March or early April.
President Joe Biden later announced the US would send 31 M1 Abrams battle tanks, marking a reversal of longstanding Pentagon arguments that they are a poor fit for the Ukrainian battlefield.
Ukrainian President Volodymyr Zelensky welcomed the move but urged the speedy delivery of the tanks. He also appealed to the West to send long-range missiles and fighter jets.
But for tanks to be "game-changer", 300 to 400 of them would be needed, an adviser to Ukraine's defence minister told BBC Radio 4's Today programme.
"The sooner we defeat Russia on the battlefield using Western weapons, the sooner we will be able to stop this missile terror and restore peace," Yuriy Sak said.
Speaking on the same programme, Nato Secretary General Jens Stoltenberg said sending tanks to Ukraine would make a big difference to the country's ability to win the war.
He also warned that Russia was planning a fresh offensive, just as reports began emerging from Ukraine of missile strikes following drone attacks overnight.
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