Russian forces fired 60 missiles and carried out drone attacks across Ukraine on Friday, officials said, striking the capital Kyiv and cities in the north, south and west.
Two people were killed and five wounded when a residential building was hit in Kryvih Rih in central Ukraine.
Attacks have intensified this week as Russia targets Ukraine's civilian infrastructure.
Power was completely down in Kharkiv in the north and several other regions.
The alarm was raised across Ukraine and air force spokesman Yuriy Ignat said in total 60 missiles had been fired. Earlier reports said drones were also involved.
Power was also out in the Sumy region close to Ukraine's northern border with Russia, as well as the central cities of Poltava and Kremenchuk.
Russia has launched more than 1,000 missiles and Iranian-made attack drones since mid-October, although most of them have been intercepted by air defence.
Ukraine has accused Russia of "weaponising winter" by striking essential facilities as temperatures plummet.
UN human rights commissioner Volker Turk warned on Thursday that further attacks on power facilities could "lead to a further serious deterioration in the humanitarian situation and spark more displacement".
Kyiv Mayor Vitaliy Klitschko said three areas of the city were hit. Damage to energy infrastructure had affected water supplies and city metro lines were for the moment not running, he said.
The head of the regional administration, Oleksiy Kuleba, said Russia was "massively attacking Ukraine".
Prime Minister Denys Shmyhal said this week that Russian strikes had damaged "all thermal and hydroelectric power plants", leading to widespread blackouts and interruptions in heating and water supplies.
In some areas, electricity is only available a few hours per day.
Fifteen rockets were reportedly fired at Zaporizhzhia in the south, while officials in the north-western Zhytomyr region said initial information suggested Russia had fired rockets and kamikaze drones at the same time.
Authorities say these attacks are Russia's response to military setbacks on the battlefield, amid Ukraine's recent successes in retaking occupied territory.
It is unclear why Russia has intensified its strikes this week, but US President Joe Biden is reportedly finalising plans to send Patriot air defence missiles to Ukraine, after months of requests from Kyiv.
Two people died in shelling in the southern city of Kherson on Thursday, but air defences in Kyiv brought down 13 drones targeting the capital on Wednesday.
Russia's war in Ukraine has been losing momentum, almost 10 months into its invasion. But Ukrainian Defence Minister Oleksii Reznikov warned there was mounting evidence that Russia was planning a broad new offensive, possibly early next year.
"The Russians are preparing some 200,000 fresh troops. I have no doubt they will have another go at Kyiv," the head of the armed forces, Gen Valery Zaluzhny, told the Economist.