Russia struck Kyiv and Kharkiv in the east, among other cities, killing at least five civilians, injuring dozens and creating widespread damage, the Reuters news agency reported.
Downed Russian rockets damaged high-rise buildings and sparked fires, killing two people in Kyiv's Solomyanskyi district, among other casualties, according to officials.
At least 60 cruise missiles and 10 Kinzhal missiles were intercepted over Ukraine's capital, the Kyiv Post website reported.
In all, Ukraine's air defences brought down 72 out the 99 missiles Russia had fired, according to officials.
Ukraine also shot down all the 35 Shahed drones used in Russia's Tuesday morning attack, the war.ukraine.ua website reported.
250,000 people went without power in the Kyiv region after the Russian strikes, the state energy operator Ukrenergo said.
The Kremlin leader Vladimir Putin on Monday said Russia would "intensify" strikes on Ukraine following Saturday's Ukrainian air attack on the Russian city of Belgorod, which Moscow said killed 25 civilians.
On Friday, Russia launched the largest attack of the war, killing at 39 Ukrainian civilians, the Reuters news agency reported.
More Russian air assaults on Ukraine followed on Sunday and on New Year's Day, according to news outlets.
Tuesday is day 678 of Russia’s war on Ukraine.
Russia invaded Ukraine on February 24, 2022, launching the largest military campaign in Europe since World War II.
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Source: Kyiv Post, Reuters, war.ukraine.ua