At least 40 people have been injured, including two children, the city's mayor said. Some 31 of those are being treated in hospital.
It marks the third day in a row Ukraine has reported deaths, as Moscow ramps up its assault after a three-day ceasefire expired on Monday.
The overnight barrage saw more than 670 drones and 56 missiles launched across the country, President Volodomyr Zelensky said. This is among the largest attacks Russia has mounted since the start of its full-scale invasion in 2022.
In the capital, a search and rescue operation began early Thursday to look for people under the rubble of a nine-storey apartment block which had been hit overnight.
Kyiv Mayor Vitaliy Klychko, who visited the building, said 18 apartments had been destroyed. He also said the attack had disrupted the city's water supply.
Zelensky said dozens had been rescued from the building so far, while damage had also been done to other residential buildings, a school, a veterinary clinic and other infrastructure.
The large-scale attack saw Russian drones fly across much of Ukraine, with the regions of Kremenchuk, Bila Tserkva, Kharkiv, Sumy, and Odesa also coming under fire, Prime Minister Svyrydenko said.
"Ukraine needs help in strengthening its air defense," she wrote on social media. "This is the only way to save our people and our cities."
Ukraine's Foreign Minister Andriy Sybiha condemned Russian President Vladimir Putin for the "barbaric attack", which he said showed Moscow was pursuing "aggression and terror" over peace.
He noted the attack had taken place during a crucial summit between US President Donald Trump and China's Xi Jinping, and urged the two leaders to exert pressure on Russia.
"I am certain that the leaders of the United States and China have enough leverage over Moscow to tell Putin to finally end the war," he said.

The latest attacks came shortly after a three-day, US-brokered ceasefire expired late on Monday.
Both Russia and Ukraine reported multiple violations during the truce - mostly along the vast frontline - but no large aerial attacks.
Russia resumed its attacks on Tuesday, killing nine people.
Six more people were killed in another major attack on Wednesday, which Ukraine's saw 892 drones launched from Russia.
On Thursday morning, Zelensky said a total of more than 1,560 Russian drones had targeted Ukrainian cities since Tuesday night.
He described Russia's huge assault as "definitely not the actions of those who believe the war is coming to an end", and urged Ukraine's allies not to remain silent.
In a separate development in Kyiv, a court has ordered 60 days' pretrial detention for Zelensky's former right-hand man, Andriy Yermak, over a corruption scandal.
The court said he could be released on bail of £2.35m ($3.2m) with an electronic tag.
Yermak has been named by Ukraine's anti-corruption agencies as a suspect in a money-laundering scheme involving £7.5m luxury construction project outside Kyiv.
His lawyer has described the allegations as "baseless".
The renewed escalation highlights the growing intensity of the war following the collapse of the temporary ceasefire, while Ukraine continues to call for stronger international support to protect its cities and civilians from ongoing Russian attacks.
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