At least two people have been killed and more than 20 injured in an airstrike in the western city of Lviv, according to the regional governor Maksym Kozystskyi.
The city’s mayor Andryi Sadovy said a number of residential buildings were on fire, with two schools to remain shut on Wednesday as a result of the attacks.
Explosions were also heard over the capital, Kyiv, early on Wednesday as air defences tried to 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.