Explosions reverberated through Kyiv just after 1am local time on Sunday, following a warning by Ukraine's air force on its Telegram channel that Russia might launch a hypersonic Oreshnik ballistic missile.
The air force did not respond to a request for comment on whether an Oreshnik struck any target during the attack.
Kyiv Mayor Vitali Klitschko said two people had been killed and 56 others injured in the attacks on the city, with 30 of those hospitalised. Some damage was reported in the city's historic Independence Square.
"It was a terrible night for Kyiv," Klitschko said in a Telegram message from the site of one attack.
"Right now, rescuers are putting out fires and clearing debris. Medics are providing assistance to the victims."
Many residents sought shelter overnight in the city's metro stations.
Nataliia Zvarych, 62, said she had rushed to her local station as explosions started rocking the city.
"It was terrifying, scary," she said.
"We have been sitting here for more than three hours now, listening to the explosions up there."
The head of the city's military administration said that more than 40 locations in the city had been damaged.
Strikes were reported in other parts of Ukraine.
A further two people were killed and nine others injured in attacks on the broader Kyiv region surrounding the capital, said regional governor Mykola Kalashnyk.
As the sun rose, black smoke from several fires drifted across the skyline, leaving an acrid smell in parts of the city.
Firefighters used hoses to douse the flames in damaged buildings while rescue workers evacuated the wounded.
The front facade of one five-storey residential building had collapsed, images showed.
Officials reported damage to offices, shops, warehouses and the foyer of a metro station.
President Volodymyr Zelenskiy had warned on Saturday that Russia was preparing a strike against Ukraine using the Oreshnik missile, citing intelligence from Ukraine, the US and Europe.
Russia has already attacked Ukraine twice with the Oreshnik, a missile with a range of several thousand kilometres and capable of carrying a nuclear warhead.
Russian President Vladimir Putin has boasted that it is impossible to intercept because of its reported velocity of more than 10 times the speed of sound.
Zelenskiy's warning came after Putin ordered his military to prepare options for retaliation against Ukraine for a drone strike on a student dorm in the Russian-occupied Luhansk region of eastern Ukraine on Friday.
Ukraine's military denied the accusations and said it had targeted a Russian drone command unit.
Neighbouring Poland activated its military aviation during the strikes on Sunday, but no violations of its airspace were detected, the Polish army said.
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