Firefighters work in an apartment building damaged by shelling in Kyiv, Ukraine, Tuesday, March 15, 2022. AP
Two bodies were pulled from the rubble after a strike on a 16-storey building in the Sviatoshynsky district, the emergency service said in a Facebook post, adding that 27 people had been rescued from the site.
Another residential building in the Podilsk area also came under attack, it said.
"A fire started on the first five floors of a ten-storey residential building on Mostytska street as a result of ammunition fire," it said.
AFP journalists said they heard at least three powerful explosions in the centre of Kyiv early on Tuesday morning.
In Podilsk, smoke was still billowing from the blackened impact site in the middle of the building, said an AFP journalist at the scene.
Shattered glass and debris were spread around the explosion site while residents were throwing charred wreckage out of their windows.
Windows were blown out by the impact from surrounding blocks.
Separately, the emergency service said a private home was hit in the Osokorky district in southeastern Kyiv.
Images shared by the emergency service showed the blackened wall of a two-storey building with smoke seeping from the shattered windows.
Fighting has intensified in recent days around Kyiv, which is almost completely surrounded by Russian forces that invaded Ukraine on February 24.
More than half of Kyiv's three million inhabitants have fled the city since the start of the Russian offensive.
Fierce fighting has been going on for several days between Russian and Ukrainian forces on the northwest outskirts of Kyiv.