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.
Eleven people died and 11 others were injured after 35 buildings were struck across several regions, the state's emergency service said.
It added the worst damage to residential buildings was in the Kyiv region.
Officials also reported strikes on two energy facilities in the Odesa region.
The barrage came as Russia said it perceived the new offer of military support, which followed a UK pledge to send Challenger 2 battle tanks, 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.
Canada has also promised to supply Ukraine with four "combat-ready" Leopard tanks in the coming weeks, together with experts to train Ukrainian soldiers in how to operate them.
Ukrainian President Volodymyr Zelensky said on Thursday that 12 countries had now joined what he called the "tank coalition".
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.
On Thursday, the US designated Russia's Wagner group, which is believed to have thousands of mercenaries in Ukraine, a transnational criminal organisation.
It also imposed fresh sanctions on the group and their associates to "further impede [Russian President Vladimir] Putin's ability to arm and equip his war machine", Treasury Secretary Janet Yellen said in the statement.