Shelling hit residential houses and a shopping district in Kyiv's Podil district late on Sunday, killing at least one person, mayor Vitali Klitschko said.
"According to the information we have at the moment, several homes and one of the shopping centres [were hit]," Klitschko said on his Telegram channel.
He said rescue teams were putting out a large fire at the shopping centre, while other details are still to be confirmed.
Reuters was not able immediately to verify the reports on the ground.
Russia's invasion of Ukraine has killed thousands of people, displaced more than 3 million and raised fears of a wider confrontation between Russia and the United States.
Russian President Vladimir Putin says the "special military operation", which started on February 24, is aimed at disarming Ukraine and rooting out dangerous nationalists.
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