The strikes overnight into Saturday 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.
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 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, the emergency services said.
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.
Lithuania's foreign minister said the country's embassy in Kyiv was damaged when missiles struck nearby.
Russia's defence ministry said on Saturday it had launched a "massive strike" against "Ukrainian military-industrial complex facilities and logistics centres in Kyiv".
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 on 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 Friday in a post on Telegram.
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 on the matter.
In other developments a Russian airstrike killed one person and wounded five more in the city of Kherson in southern Ukraine, local officials said on Saturday.
In Russian-occupied Crimea, the Moscow-appointed head of the city of Sevastopol, Mikhail Razvozhayev, said a woman was killed and two other people wounded in a drone attack on the city.
Ukrainian drones struck three Russian oil refineries overnight in the Russian republic of Bashkortostan, Zelenskyy said on Saturday.
The refineries "process millions of tons of oil each year" and are located nearly 1600km from Ukraine, Zelenskiy said
Ukraine's almost daily long-range drone and missile strikes using domestically developed weapons have battered Russian oil facilities for months. The operation has brought a fuel crisis that is embarrassing the Kremlin more than four years after Russia's all-out invasion of its neighbour.
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