Tymur Tkachenko, the head of Kyiv’s military administration, said one person was killed and 16 others were wounded in the barrage on the city.
Ukraine’s state emergency service later reported 31 people, including a child, had been wounded in strikes across the Kyiv region.
Military authorities said the strikes hit six districts of the capital and six more in the surrounding region.
At daybreak, AFP journalists saw rescue workers searching for survivors in the rubble of destroyed buildings in Kyiv.
Rescuers were seen hauling a wounded person from a partially collapsed residential building.
Ukraine’s emergency service said those search and rescue operations were ongoing.
Strikes from both Moscow and Kyiv resumed after Russia ended a three-day ceasefire with Ukraine on Tuesday.
United States President Donald Trump had announced the pause last week, hours before Russian leader Vladimir Putin presided over a scaled-down military parade in Red Square to mark the anniversary of victory in World War II.
Zelensky has urged Trump to discuss ending the conflict during his meetings this week with Chinese leader Xi Jinping.