A five-storey residential building in Kyiv's Solomianskyi district was damaged by falling debris and a fire broke out.
Rescue workers evacuated 35 people from the upper floors of the building 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 on Saturday.
Elsewhere, emergency workers extinguished a fire in a non-residential building in the capital's Shevchenkivskyi district.
There was no additional information about earlier reports by the district mayor that people were trapped in another residential building.
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.
The Ukrainian leader late on Friday said he spoke to US Vice-President JD Vance and discussed a meeting with President Donald Trump on Tuesday 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 Friday in a social media post.
At a NATO summit in Ankara in July, Trump said the US would give Ukraine a licence 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.
Saturday's attack on Kyiv came just two days after a large-scale Russian ballistic missile and drone attack across Ukraine killed 10 civilians and wounded more than 50 others and saw a Russian missile enter Polish airspace.
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."
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