At least 21 people were killed and 112 wounded in shelling in the eastern Ukrainian city of Kharkiv in the last 24 hours, regional governor Oleg Synegubov said on Wednesday.

The authorities have said Russian missile attacks hit the centre of Ukraine's second-largest city, including residential areas and the regional administration building, as Moscow started day six of its invasion.

Synegubov said Russia launched GRAD and cruise missiles on Kharkiv but that the city defence was holding.

"Such attacks are genocide of the Ukrainian people, a war crime against the civilian population!" he said.

Wearing a flak jacket and a helmet, Synegubov said in a video posted on social media on Tuesday morning that it was too early to know the number of casualties.

He shared a video showing Kharkiv regional administration building being hit by a missile and exploding. Reuters verified the authenticity of the video.

Russia calls its actions in Ukraine a "special operation" that it says is not designed to occupy territory but to destroy its southern neighbour's military capabilities and capture what it regards as dangerous nationalists.