In Kharkiv, five people were injured in artillery fire on a residential area, Mayor Ihor Terekhov said on Telegram.
In Vovchansk, Russian attacks caused severe damage.
"Unfortunately, the city of Vovchansk has been practically destroyed by the enemy, who are mercilessly attacking with glide bombs," Security Council member Andrey Kovalenko said on Telegram.
Ukraine is managing to retain control of Vovchansk despite the repeated attacks, he added.
The city in northeast Ukraine had nearly 19,000 inhabitants before the war.