Zelensky added that beyond Kyiv, substations were damaged in Vinnytsia, Zhytomyr, Rivne, Kharkiv and Dnipro regions.
The latest attacks come after US First Lady Melania Trump hosted Russian and Ukrainian delegations at the White House on Thursday.
She called for a “more enduring” ceasefire in Ukraine following a truce last week in the southern region of Kherson.
She thanked both Zelensky and Russian President Vladimir Putin, making no reference to the origins of the war, which began when Putin launched a full-scale invasion of Ukraine in February 2022, which has caused thousands of civilian casualties and the displacement of millions.
Hundreds of residents of the Russian-occupied Ukrainian town of Oleshky facing starvation and constant bombardment were able to evacuate during a six-day ceasefire, which both Moscow and Kyiv credited Trump with brokering.
“The lives of innocent people must transcend the division of war. I hope Oleshky inspires greater peace,” she said.
Earlier this week, a number of people were killed when glide bombs hit an aid centre near Zaporizhzhia, with the death toll rising to 55 as teams search deeper into the ruins.
Zelensky added in his Telegram post on Saturday following the latest attacks that Ukraine was counting on increased bilateral support from the United States.
He wrote: “We are counting on unity between both parties on issues of security, support for Ukraine, condemnation of Russian aggression, and increased sanctions pressure on Putin.
“The resolve and consistency of the United States in supporting Ukraine are of great importance in bringing peace closer.”
Meanwhile, Zelenksy’s spokesperson would not be drawn on reports that the Ukrainian president is to be invited to the UK for a state visit next year.
Additional reporting by Daniel Wittenberg
