In the first waves of Russia's attacks, at least six missiles hit Kharkiv, Ukraine's National Police said on Sunday, injuring at least 22 people and hitting 12 apartment buildings, 13 residential houses and a kindergarten.
Earlier, Ukrainian officials said that among those injured in Kharkiv were two boys aged 14 and 16 and a security adviser for a team of German journalists.
Closer to midnight, as part of a wider bombardment of Ukraine that also targeted Kyiv, several waves of Russian drones hit residential buildings in Kharkiv's centre, spouting fires, the mayor of Kharkiv, Ukraine's second-largest city, said.
"On the eve of the New Year, the Russians want to intimidate our city, but we are not scared - we are unbreakable and invincible!" the mayor, Ihor Terekhov, said.
The attacks came within hours after what Moscow said was an "indiscriminate" Ukrainian air attack on the city of Belgorod, near Kharkiv and just north of Ukraine's border, that killed at least 22 people.
Russian newspaper Kommersant cited a source close to the Russian Investigative Committee as saying that Ukraine launched its attack on Belgorod from a multiple rocket launcher in the Kharkiv region.
Terekhov posted several photos showing windows blown out of residential buildings and fire fighters putting out a fire at what seemed like a store.
Both sides have increased attacks in the last week of 2023, with Russia killing at least 31 civilians in its biggest air assault of the war on Ukraine on Friday.
US President Joe Biden, asked if he'll speak to Ukraine's President Volodymyr Zelenskiy after Russia's latest attacks in Ukraine, said: "I speak to him regularly."
