Rescue crews were pulling residents from buildings shattered by the overnight barrage, Kyiv's Mayor Vitali Klitschko said on Monday.
"From a building in the Podilskyi district, where a partial collapse occurred, rescuers evacuated 15 people," he wrote on Telegram.
"Three women and six children were taken down from the upper floors."
Tymur Tkachenko, head of Kyiv's City Military Administration said on Telegram several multi-storey buildings were damaged and people were believed to be trapped under the rubble in the Darnytsia district.
Tkachenko also said three apartment buildings had been hit in the eastern Darnytskyi district, where many died in a strike last Thursday, when Russia launched hundreds of drones and dozens of missiles at the city, killing at least 30 people.
"These are residential buildings. Places where people slept and lived their ordinary lives," he said.
The overnight attack which was still underway early Monday morning, involved waves of ballistic and cruise missiles as well as drones. Explosions echoed across the city as civilians sought shelter in metro stations.
Ukrainian President Volodymyr Zelenskyy had warned hours earlier of another large-scale Russian attack on the city.
Reuters witnesses reported a series of explosions in and around the capital and said air defences were in action against Russian drones.
Pictures posted on unofficial Telegram channels showed several high-rise apartment buildings and a commercial building ablaze after being struck. Other pictures showed serious damage to building interiors.
Bloggers told residents to shut their windows as smoke settled over the city. Residents crowded into shelters in the city's metro and in underground parking garages.
Zelenskiy renewed calls for Western partners to bolster Ukraine's air defences, particularly by supplying more Patriot missiles, saying that failing to replenish them only emboldens Russia to prolong its four-year war.
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