The overnight bombardment, which included 11 ballistic missiles, targeted critical infrastructure and residential areas across eight regions of Ukraine, Zelenskiy said on Thursday.
Dozens of people, including children, were injured, officials said, though authorities did not immediately publish a confirmed total.
Zelenskiy said late on Wednesday he had spoken by phone with US President Donald Trump and thanked him for his "efforts and engagement" in pursuing peace negotiations.
The US-brokered talks between Moscow and Kyiv are continuing but are deadlocked on the issue of the future of Ukrainian territory that Russia claims as its own.
Trump representatives Steve Witkoff and Jared Kushner, who were also discussing nuclear negotiations with Iran in Geneva before turning to the war in Europe, were due to meet Rustem Umerov, the head of Ukraine's National Security and Defence Council.
They also joined Trump's call with Zelenskiy.
Washington is looking to keep momentum in its year-long push to stop the fighting and overcome deep enmity between the warring countries.
Ukrainian and European officials have accused Russian President Vladimir Putin of feigning interest in peace negotiations, hoping to avoid punitive US measures such as additional sanctions while pressing forward with the invasion.
Thursday's talks between the American and Ukrainian envoys were to address details of a possible postwar recovery plan for Ukraine and discuss preparations for an upcoming trilateral meeting with Moscow officials, perhaps next week, according to Zelenskiy.
He said he had also tasked Umerov with discussing a possible prisoner exchange.
Russia returned 1000 bodies of fallen soldiers to Ukraine, and received 35 bodies of its fallen troops, Vladimir Medinsky, the head of the Russian delegation at previous talks with Ukraine, said on Thursday.
He did not say when the exchange happened.
Russia struck gas infrastructure in the Poltava region and electrical substations in the Kyiv and Dnipropetrovsk regions, Zelenskiy said.
Emergency crews responded in five other regions, as well as in the capital.
Ukraine's air defences shot down most of the Russian missiles, Zelenskiy said, crediting Western partners for timely delivery of additional air defence interceptors.
Ukrainian Foreign Minister Andrii Sybiha urged allied countries to provide more military aid.
"When the whole world demands Moscow to finally stop this senseless war, Putin bets on more terror, attacks and aggression," Sybiha said in a post on the Ministry of Foreign Affairs website.
