About 15 blasts were heard in Ukraine's Kharkiv on Friday morning, mayor Ihor Terekhov said, and Russian missile strikes appeared to be targeting the city's power supply, causing partial blackouts.
Terekhov did not report any casualties. He said some of the city's water pumps had stopped because of the attacks.
In central Ukraine, Kryvyi Rih mayor Oleksandr Vilkul said blasts were heard in the city, but provided no details.
In another central Ukrainian city, Vinnytsia, a "critical infrastructure object" has been damaged, according to mayor Serhiy Borzov.
The administration of the southern Ukrainian city of Zaporizhzhia also reported eight missile strikes and said some locals had been wounded.
According to Ukrainian officials, several Russian missiles were still moving towards targets in Ukraine.