Shelling was heard in the northern part of Kharkiv on Thursday afternoon while smoke billowed from residential neighbourhoods.
At least one house was destroyed, and others were set on fire by the shelling.
Other houses were on fire in the early afternoon as the result of the shelling.
Associated Press journalists saw an ambulance collect four bodies near the remnants of rockets.
Outgoing artillery shots fired by Ukrainian forces could also be heard during the day.