The heaviest death toll was in Pryluky in Ukraine's northern Chernihiv region, where a Russian missile obliterated a five-storey residential building.
Zelenskiy said 19 people died in the attack, including five children.
He said 25 people had been killed in the strikes throughout the country, with 100 injured.
Interior Minister Ivan Vyhivskyi put the death toll at 28.
The president noted that the attacks coincided with Russian President Vladimir Putin's birthday.
"This is the kind of birthday present that Putin gave himself: the killing of children, the killing of people," Zelenskiy said in his nightly video address.
In earlier online comments, Zelenskiy said civilians had also been killed in the capital Kyiv and in the central cities of Oleksandria and Kremenchuk during the massive attack.
In total, Russia fired 70 missiles at Ukraine overnight - many of them high-velocity ballistic munitions - and dozens of Shahed attack drones, he said.
"The Russians wanted to strike painfully and demonstratively. This was one of the most vile strikes."
In Pryluky, an excavator and dozens of rescuers with shovels sifted through rubble at the site where several sections of the apartment block had collapsed.
Emergency workers used ladders to get to the upper floors of what remained of the building and brought out 15 survivors as they worked their way down through the rubble.
About 55 people were wounded in the town, regional officials said.
"There's a lot of destruction, especially in the town centre," said Danylo Savenko, deputy mayor of Pryluky, who said he had run to an air raid shelter with his wife as soon as he heard the missiles flying.
Russia's defence ministry said its forces had carried out a "massive strike" on military-industrial facilities in Kyiv and other Ukrainian regions using high-precision land-, sea- and air-launched weapons as well as drones.
Ukraine's air force said it had downed about 80 per cent of the 46 jet-powered drones launched by Russia - a sharp increase from recent weeks when, on average, air defences took down 50 per cent to 60 per cent.
Since the northern hemisphere summer, Russia has used increasing numbers of the new high-velocity drones in round-the-clock attacks on Kyiv and other cities, with Ukraine's air defences struggling to cope with their speed.
The air force did not explain the jump in the interception rate and did not immediately respond to requests for comment.
Zelenskiy said the Russian ballistic missiles remained the major challenge for Ukraine, adding that he and his team were "every day looking for Patriot (missile interception) systems that can and must protect people's lives".
Ukraine received a new 1.2 billion euro ($A1.9 billion) tranche from the European Union on Wednesday and will channel the funds towards defence needs, Prime Minister Sergii Koretskyi said.
The US-made Patriot system is the only weapon in Ukraine's arsenal capable of stopping high-velocity ballistic missiles but tight global supplies have been drained by the Iran war as well as the Ukraine conflict.
Russia's defence ministry said its targets included sites where Ukrainian defence company Fire Point manufactures and stores its Flamingo cruise missiles and medium- and long-range drones in Kyiv as well as regions of Kyiv, Chernihiv, Kirovohrad, Dnipropetrovsk, Poltava and Kharkiv.
Last week Zelenskiy said Ukraine had fired its first domestically made ballistic missile in combat, produced by Fire Point.
In an interview with Reuters, he said he expected the company to have a longer-range FP-9 missile ready by the autumn.
Fire Point has said that weapon will be able to reach Moscow.
