Ukrainian President Volodymyr Zelensky says Russia made a "conscious choice" by launching a major overnight attack on his country's energy infrastructure on Christmas Day.
Ukraine's air force said it had detected 184 missiles and drones, but many were shot down or missed their targets.
It said there were casualties from the strikes but gave no figures.
Moscow confirmed the attack and claimed that its goal had been achieved.
Russia's defence confirmed its forces had carried out a "massive strike" on "critical" energy facilities in Ukraine.
It added that the strike had been a success and all targets were hit.
This was the 13th major attack on Ukraine's energy sector this year, the country's largest private energy company, DTEK, said.
Responding to the latest Russian strikes, US President Joe Biden said: "The purpose of this outrageous attack was to cut off the Ukrainian people's access to heat and electricity during winter and to jeopardise the safety of its grid."
Biden - who will be succeeded by Donald Trump on 20 January - also asked the US defence department to continue delivering weapons to Ukraine.
In September, President Zelensky said 80% of Ukraine's energy infrastructure had been destroyed by Russian bombs.
Responding to Wednesday's attacks, Zelensky said the timing had been a "conscious choice".
He called them "inhumane" and said work was being done to restore power as soon as possible.
"Russian evil will not break Ukraine and will not distort Christmas", he added.
This is the second time Ukraine has celebrated Christmas Day on 25 December. It traditionally followed the Julian calendar, like Russia, where Christmas falls on 7 January.
Still, a sizeable number of Orthodox believers in the country will be celebrating Christmas as before.
In the north-eastern city of Kharkiv - Ukraine's second largest - the attack left half a million people without water, electricity or heating in bitterly cold temperatures, the regional head said.
Ukrainians across the country woke up to the sound of air raid alarms, and were told to shelter as the attacks unfolded in the morning.
Kyiv residents sheltered in metro stations, with one local telling Reuters news agency that she felt angry and frightened.
"Of course, I want to be at home and celebrate, but we had to shelter because it's scary to stay at home," Sofiia Lytvynenko said.
Another Kyiv resident, Oleksandra, said that despite the attack, "Christmas is not cancelled".
She told Reuters that she planned to enjoy traditional Ukrainian food and drink with family and friends after it is safe to leave the shelter.
Ukraine's state-owned power company, Ukrenergo, warned Ukrainians that power cuts could last until at least the end of the day.
It has imposed usage restrictions while it tries to restore service.
Meanwhile, Ukrainian Foreign Minister Andrii Sybiha described the strikes as "Christmas terror".
He said a Russian missile went through Moldovan and Romanian airspace "reminding that Russia threatens not only Ukraine".
Moldovan President Maia Sandu condemned the strike and confirmed that a missile was detected in the country's airspace.
Romania said it did not detect a missile in its airspace.
Elsewhere, four people were killed and five others injured by Ukrainian shelling in Russia's Kursk region, according to the region's acting governor.
