Russia on Tuesday rained missiles on the Ukrainian capital and other cities killing two people and injuring over 50 as strikes damaged high-rise buildings and sparked fires.
The attacks came less than 24 hours after Russian President Vladimir Putin said Moscow would intensify strikes on Ukraine.
Ukraine said Russia fired 99 missiles but it had downed 72 of them.
"The enemy used 99 air attack weapons -- missiles of various types," commander-in-chief Valery Zaluzhny said on social media, adding that the air force "destroyed 72 air targets."
Barrages of loud explosions were heard in Kyiv by AFP journalists on Tuesday morning from around 0500 GMT as air defences worked, shaking buildings in the city centre.
Kyiv Mayor Vitaly Klitschko said one person was killed and 20 wounded in the capital.
Authorities said missiles caused fires in a supermarket building, residential houses and a market, in several districts in Kyiv.
The air raid alert in the capital lasted almost four hours. 250,000 people in the region ended up without power.
In the eastern city of Kharkiv, one woman was killed and 41 wounded by "at least four strikes" that damaged multi-storey buildings and civilian infrastructure in the centre, the head of the city's military administration, Oleg Sinegubov, said.
The Ukrainian air force said Russia was launching Kinzhal missiles.
Tuesday's attacks came after an escalation in the war in recent days, with both sides hitting each other with deadly attacks.
Putin on Monday called an unprecedented Ukrainian attack on the Russian city of Belgorod a "terrorist act" and vowed retaliation.
Moscow also attacked Ukraine with a barrage of drones on New Year's Eve.
Ukraine is seeking assurances from its supporters that military aid will continue as the US has released its last tranche under current authorisations and the Republicans are blocking new aid.
- 'Critical we support Ukraine' -
"Putin is ringing in 2024 by launching missiles at Kyiv and around the country as millions of Ukrainians take shelter in freezing temps. Loud explosions in Kyiv this morning," US Ambassador to Ukraine Bridget Brink wrote on X.
"It's urgent and critical that we support Ukraine now -- to stop Putin here."
Kyiv mayor Klitschko reported multiple explosions and debris from downed missiles hitting the capital as residents were advised to stay in underground shelters.
He said 16 people had been injured in a multi-storey block of flats in the Solomiansky district "where a fire broke out as a result of a missile attack".
In the Pechersk district, debris hit the roof of a nine-storey building and another multi-storey building, the military administration said,
Fires also broke out in a supermarket and a warehouse measuring 2,000 square metres, the mayor said.
In the city's northern Podil district, "the territory of a civilian infrastructure facility is believed to have been hit", Klitschko said.
Some civilian infrastructure and residential buildings in four districts were without power, the mayor said, while a gas pipe had been damaged in one district.
"As soon as the security situation allows it, we will definitely restore electricity to everyone," the city's military administration said.
In the city's Podil district, mains water pipes have been damaged, it added.
The attacks came after Russia on December 29 launched a wave of strikes across Ukrainian cities, including Kyiv, which killed 39 people.
Moscow also hit Ukrainian cities on New Year's Eve, with Kyiv saying it had foiled a "record" number of drones launched by Russia.