At least 10 people were killed and 35 hurt when the opera house, concert hall and government offices were hit in Freedom Square in Kharkiv.
Speaking to the European Parliament, Mr Zelensky urged the EU to prove it was with Ukraine.
Later the main TV tower in the capital Kyiv was hit, putting media off air.
Footage on social media showed smoke billowing from the steel structure.
Five people died in the attack, Ukrainian officials said, but the tower remains standing.