Kyiv Mayor Vitali Klitschko said on Saturday one person was killed in the capital city and four injured, including three being treated in hospital.
Klitschko said the strikes had triggered fires in districts on either side of the Dnipro River, which bisects the capital.
He said heating and water supplies had been disrupted in parts of the city east of the river.
Ukraine's air force said both drones and missiles had been deployed in the assault on the capital.
Tymur Tkachenko, head of Kyiv's military administration, reported strikes in at least four districts. A medical facility was among the buildings damaged.
Kyiv has already endured two mass overnight attacks since the New Year that have knocked out power and heating to hundreds of residential buildings.
Emergency workers were still restoring services to residents, with overnight temperatures dipping to minus 13C.
In Kharkiv, a frequent target 30km from the Russian border, Mayor Ihor Terekhov said 25 drones had hit several districts in less than three hours, with at least 11 people injured.
Writing on Telegram, Terekhov said the drones had struck a dormitory for displaced people, a hospital and a maternity hospital.
The latest attacks occurred after negotiators from Ukraine, Russia and the US completed the first of two days of talks in the United Arab Emirates aimed at finding a resolution of the almost four-year-old war.
Ukrainian and Russian negotiators have met in Abu Dhabi to tackle the vital issue of territory, with no sign of a compromise.
Ukraine is under mounting US pressure to reach a peace deal in the war triggered by Russia's full-scale invasion in February 2022, with the Kremlin demanding Ukraine cede its entire eastern industrial area of Donbas before it stops fighting.
Ukrainian President Volodymyr Zelenskiy said the territorial dispute would be a top priority of the talks.
"The question of Donbas is key. It will be discussed how the three sides ... see this in Abu Dhabi today and tomorrow," he told reporters in a WhatsApp chat a day after talks with US President Donald Trump at the World Economic Forum in Davos.
The negotiations in the Gulf are expected to continue on Saturday morning, Zelenskiy's aide said.
The talks unfold against a backdrop of intensified Russian strikes on Ukraine's energy system that have cut power and heating to major cities like Kyiv as temperatures hover well below freezing.
Russian President Vladimir Putin's demand that Ukraine surrender the 20 per cent it still holds of the Donetsk region of the Donbas - about 5000sq km - has proven a major stumbling block to a breakthrough deal.
Zelenskiy refuses to give up land that Russia has not been able to capture in four years of grinding, attritional warfare.
Polls indicate little appetite among Ukrainians for territorial concessions.
35°C