The overnight strikes follow a major Russian attack two days earlier that killed at least 10 people and wounded more than 50 others across Ukraine, as Moscow apparently looks to exploit Kyiv's critical shortage of Western-supplied anti-ballistic missile defences.
The relentless cycle of attacks dims the potential of reaching a diplomatic end to Russia's more than four-year-old invasion of its neighbour.
Russia's defence ministry said on Saturday it had launched a "massive strike" against "Ukrainian military-industrial complex facilities and logistics centres in Kyiv".
A five-storey residential building in the city's Solomianskyi district was damaged by falling debris and a fire broke out.
Rescue workers evacuated 35 people from the upper floors and two people died, with eight reported injured, including two children, according to Ukraine's state emergency service.
In the Darnytskyi district of Kyiv, seven people were killed and another 14 injured after the attack caused fires and damage to houses, vehicles, an administrative and non-residential building, emergency services said.
Elsewhere, emergency workers extinguished a fire in a non-residential building in the capital's Shevchenkivskyi district.
Damage to commercial and residential buildings was reported in two other city districts.
President Volodymyr Zelenskiy has pressed the United States and other Western partners over Ukraine's need for more Patriot anti-ballistic missile defence systems to counter missile attacks from Russia.
"Every package of ballistic missile interceptors saves the lives of our people. And every night without them results in more casualties," he wrote on X following the latest attacks.
The Ukrainian leader late Friday said he spoke to US Vice-President JD Vance and discussed a meeting with President Donald Trump earlier this week in Washington, which Zelenskiy described as "positive and productive".
"The Russian air strikes on our country continue and air defence, specifically interceptors for Patriot systems against ballistic missiles, remains a top priority," Zelenskiy said in a social media post.
At a NATO summit in Ankara in July, Trump said the US would give Ukraine a license to make Patriot systems, but he appeared to move away from that commitment on Friday during a cabinet meeting at the presidential retreat in Camp David, Maryland, saying he had not yet made a final decision on the matter.
From a basement shelter where she was taking cover as a second air alarm sounded for another wave, Liudmyla Nakonechna, 64, described how she was woken by loud explosions at 1.30am.
"I ran into the corridor and was standing there when the bathroom door was blown off its hinges and struck me in the leg," said Nakonechna, whose health is poor after undergoing cancer treatment.
"I heard the sound of shattering glass. My balcony was covered in glass and it was completely blown apart, while the windows in my bedroom were also blown out."
Nakonechna had not taken cover in a shelter since Russia's full-scale invasion on February 24, 2022, but the stress became too much, she said.
"It's getting worse by the day," Nakonechna said.
"Whereas before there was an attack once every two weeks, or maybe once a week, now it happens practically every day. It is incredibly hard to bear this psychologically."
Lithuania's foreign minister said the country's embassy in Kyiv was damaged when missiles struck nearby overnight.
In Russian-occupied Crimea, the Moscow-appointed head of the city of Sevastopol, Mikhail Razvozhayev, said on Saturday that a 60-year-old woman was killed and two other people wounded in a drone attack on the city.
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