Reuters witnesses reported a series of explosions in and around the capital early on Monday, with air defences in action against Russian drones.
Mayor Vitali Klitschko, writing on Telegram, said a residential building had been hit in the historic Podil district.
"People are trapped on the seventh to ninth floors," Klitschko said.
Drone debris had fallen on a second residential building in the same area and in other districts of the city of three million, he said.
At least 30 people were killed in Kyiv on Thursday when Russia launched hundreds of drones and dozens of missiles at the city.
Meanwhile, Russia's defence ministry says Ukraine is refusing to halt shelling of the town of Kostiantynivka in the east of the country to allow Russia to hand over the bodies of fallen Ukrainian soldiers.
Russian army commanders told President Vladimir Putin on Friday that Russian troops had taken control of Kostiantynivka although Ukraine denied the claim, saying its forces remained in control of the town.
Kostiantynivka is a key locality whose capture Russia has long sought in its military campaign in the Donetsk region.
Russia said it had proposed a six-hour ceasefire in and around Kostiantynivka on Monday to facilitate the handover of Ukrainian servicemen's bodies and had given Ukraine until Sunday morning to respond.
Ukraine's defence ministry and general staff did not immediately respond to an emailed request for comment.
Ukrainian authorities said on Sunday both Ukraine and Russia again caused a number of casualties and damage on both sides in mutual attacks.
Russia's Gvardeyskoye military airfield on the occupied Crimean Peninsula was attacked during the night, Ukraine's General Staff said on Telegram.
The extent of the damage was initially unclear.
For the Russian military, the airfield is considered the most important base in Crimea.
Ukrainian troops also attacked key transport routes for Russian resupply.
Among other things, two road bridges in the Donbas were destroyed.
The Ukrainian General Staff gave no information about the weapons used.
Russian troops targeted various sites in the eastern Ukrainian city of Kharkiv in the afternoon.
At least one person was killed and 11 others injured in attacks using drones and missiles, Kharkiv governor Oleh Syniehubov said on Telegram.
US President Donald Trump will meet Ukrainian President Volodymyr Zelenskiy on the sidelines of a NATO summit on Wednesday, a US spokeswoman said on Sunday.
The two-day summit of the NATO military alliance begins on Tuesday in the Turkish capital Ankara.
Neither Russia nor Ukraine is making any significant military progress as their mutual attacks penetrate deep into each other's territory, a senior US official stressed to reporters.
"So the president feels a real sense of urgency to try to bring this to a stop," the official said.
The US is confident that progress could be made when Trump and Zelenskiy meet.
Trump would also get in touch with Putin, the official said.
At the NATO summit, Ukraine is also to receive a new pledge of military aid worth billions of euros.
Representatives of the alliance's 32 member states agreed on this in Brussels a few days before the top-level meeting during final deliberations on the planned summit declaration.
with DPA
6°C