He added that the Zaporizhzhia, Khmelnytskyi, Sumy, Mykolaiv, Chernihiv and Odessa regions were also affected.
Zaporizhzhia Governor Ivan Fedorov said 34 people were injured in the region, including three children, two boys aged 11 and 12 and a nine-year-old girl.
One boy was caught in an explosion while the other suffered carbon monoxide poisoning, he said. Both are in serious condition.
The regional governor of Sumy said a 59-year-old man died in strikes the day before.
Zelensky promised that Ukraine would “retaliate” in a bid to “force diplomacy” from Russia, and said he counted on a “strong reaction” from Europe and the United States.
“This despicable attack actually took place at the end of the UN General Assembly week, and this is how Russia declares its true position,” he said.
Zelensky reiterated his support for US President Donald Trump's threat of tougher sanctions against Russia, as well as his call for European allies to limit their imports of Russian oil and gas.
Trump has recently changed his position on the war, saying for the first time last week that he believed Ukraine could regain land it had lost from Moscow as Russia's economy reeled under the strain of a prolonged war.
The US president has so far refrained from imposing new sanctions on Russia, but has become increasingly frustrated by the Kremlin's unwillingness to begin peace talks.
