"A massive enemy drone attack on Kyiv," Mayor Vitali Klitschko said in a post on the Telegram messaging app early on Sunday.
A woman died after falling debris from a destroyed drone sparked a fire in a high-rise residential building the capital's Dniprosvkyi district, the emergency service posted on the Telegram messaging channel. At least 27 were evacuated from the building.
Another person died in the overnight attack on Kyiv's Holosiivskyi district, the service said.
Emergency services were dispatched to several districts of the city where fires were reported.
Falling debris from a destroyed drone sparked fires in high-rise apartment buildings in the historic Podil district and the Dniprovskyi district across the Dnipro River, Timur Tkachenko, head of Kyiv's military administration, said on Telegram.
Moscow promised a break in attacks against Ukraine's energy infrastructure following talks with US President Donald Trump.
Since those statements however, the Russian military has been increasingly attacking civilian targets in Ukrainian cities.
US negotiators on Monday are due to meet separately with Ukrainian and Russian delegations in Saudi Arabia to discuss a potential ceasefire.
Late on Saturday, the Russian military launched several drone swarms against targets in Ukraine. Airstrikes were also carried out with guided glide bombs.
The industrial city of Zaporizhzhya in south-eastern Ukraine was hit by at least four bombs, military administrator Ivan Fedorov said.
This caused a fire, and several villages lost power, he said, without providing further details or information. "The shock wave and debris also damaged several private homes," he continued.
There was no immediate comment from Russia.
Meanwhile, a drone attack killed one person in a car in Russia's Rostov region, the acting governor of the southern Russian region said on Sunday.
"A car caught fire due to a drone attack," acting Governor Yuri Slyusar said in a post on the Telegram messaging app.
"A person in the car was killed."
Both sides deny targeting civilians in the three-year-long war that Russia started with its full-scale invasion on Ukraine.
The United States is pushing for a peace deal between Ukraine and Russia, and hoping to agree on a partial ceasefire that would halt strikes on energy infrastructure. But both sides have been reporting continued strikes.
Kyiv, its surrounding region and the eastern half of Ukraine were under air raid alerts for more than five hours, starting late on Saturday, according to Ukraine's Air Force maps.
President Volodymyr Zelenskiy earlier met top military commanders in the country's northeast
Zelenskiy was shown on the media platform X on Saturday with commanders in Ukraine's second largest city, Kharkiv, a frequent target of Russian attacks.
He said he discussed frontline sectors in Ukraine's east as well as in western Russia's Kursk region, where Ukrainian troops remain seven months after a cross-border incursion.
with dpa