Ukrainian media reported that hypersonic Kinzhal missiles were among the weapons used.
The Ukrainian Air Force stated that four guided missiles were intercepted.
There were also reports of explosions in the capital Kiev as the air defence was reportedly employed to counter the attacks.
A Russian missile struck an apartment building in the Ukrainian port of Mykolaiv early on Tuesday.
“After the terrorist attacks in Vinnytsia, Mykolaiv, Chasiv Yar, etc., the pressure must be increased, not decreased,” Mr Zelensky said.
A bit further south, however, Russian units at Spirne had advanced further towards the town of Siversk with massive artillery support and air force deployment.
“The secretary-general strongly urges all parties to enact an urgent and immediate humanitarian ceasefire.”
The UN warns that no fewer than 6.5 million people are now internally displaced in Ukraine in two attacks on health facilities by Russia.
