Reuters witnesses reported a series of explosions on Friday, with one of them reporting a large fire at a site where one drone had fallen.
"Enemy drones are approaching one after the other on approaches to the capital from different directions and in the city's airspace," Tymur Tkachenko, head of the city's military administration, wrote on the Telegram messaging app.
Tkachenko said drone fragments had been spotted in three districts on opposite sides of the Dnipro River that bisects the city. One drone had fallen on a building, he said.
He said details on damage and possible casualties were being collated.
Ukraine used drones to strike Russian heavy bomber planes at air bases in Siberia and the far north at the weekend, and Russia also accused it of blowing up rail bridges in the south of the country, killing seven people.
US President Donald Trump downplayed prospects for an immediate peace between the countries.
Trump said during a more than two-hour-long call with Russian President Vladimir Putin on Wednesday he urged him to refrain, but fully expected Moscow to strike back.
"It's probably not going to be pretty. I don't like it," said Trump, who described what he called "great hatred" between Putin and Ukraine's President Volodymyr Zelenskiy.
The Kremlin confirmed Putin had told Trump that Moscow was obliged to retaliate.
Trump began his second term in January vowing to swiftly end Russia's three-year-old war in Ukraine, but the deadliest conflict in Europe since World War II is instead intensifying. On Thursday he downplayed prospects for any immediate peace.
"Sometimes you see two young children fighting like crazy, they hate each other and they're fighting in a park," he said.
"Sometimes you're better off letting them fight for a while and then pulling them apart."
Trump said he believed that "at some point" there would be peace between Russia and Ukraine.
When asked if he would impose further sanctions on Russia, he responded: "When I see the moment where it's not going to stop ... we'll be very, very, very tough. And it could be on both countries to be honest. You know, it takes two to tango."
Kremlin spokesman Dmitry Peskov, at his daily briefing with reporters, highlighted comments made by Putin a day earlier about the railway attacks.
"The president described the Kyiv regime as a terrorist regime, because it was the regime's leadership that consciously gave the order, the command, the order to blow up a passenger train. This is nothing other than terrorism at the state level. This is an important statement by the president," Peskov said.
Russia has not yet provided evidence that Ukrainian leaders ordered the rail attacks, and Kyiv has not acknowledged responsibility.
Ukrainian attacks inside Russia and Russian air strikes and advances on the battlefield have escalated the war that began in February 2022, damaging prospects for peace talks that the two sides resumed in Turkey in May.
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