Bombs landed in the city's central square, striking the building that houses the headquarters of the city's administration.
The city of 1.4 million, which is predominantly Russian-speaking, is one of Putin's key targets in taking Ukraine. It is now believed to be surrounded by Russian troops on all sides as they prepare to mount an incursion into the city centre.
Kharkiv’s mayor Igor Terekhov has said that Russian forces are "everywhere around the city."
"This morning the central square of our city and the headquarters of the Kharkiv administration was criminally attacked," said the region's governor Oleg Sinegubov. "Russian occupiers continue to use heavy weaponry against the civilian population."
In the nearby region of Sumy, close to the Russian border, 70 Ukrainian soldiers are reported to have been killed in the bombing of a military facility by Russian forces.
"Many died," said the region's head Dmytro Zhyvytsky. "Currently, places are being prepared in the cemetery for about 70 dead Ukrainian soldiers."
The civilian death toll is now being reported by Ukrainian officials at over 350, with Russia continuing to deny its forces are targeting civilian areas.
Citizens of Ukraine's capital Kyiv are preparing for an imminent assault on their city, with satellite images revealing a 65km long Russian convoy making its way towards the capital.
