Maksym Kozystskyi, the regional governor, reports that an airstrike in the western city of Lviv has left at least two persons dead and over twenty injured.
According to the city's mayor, Andryi Sadovy, several residential structures were on fire, and as a result of the attacks, two schools will be closed on Wednesday.
Early on Wednesday, sounds of explosions came from the capital city of Kyiv as air defenses attempted to bring down Russian missiles.
The Ukrainian military said the whole country has been placed under an air alert.
The latest attacks come a day after 51 people were killed by Russian air strikes in the city of Poltava.
Rescue workers are continuing to search through the rubble of a military institute in Poltava for survivors of Tuesday's attack.
People did not have enough time to get to bomb shelters after the air raid alarm sounded, Ukraine's ministry of defence said, as 51 people were killed and hundreds of others injured.
President Volodymyr Zelensky promised that what he called "Russian scum" would pay for the attack, and repeated calls for more air defences so that Ukraine could protect itself by carrying out its own long-range missile attacks.
Moscow has not commented on the attack.