Moscow has stepped up a winter campaign of strikes on the Ukrainian energy system while also waging a battlefield offensive as Kyiv faces US pressure to secure peace in the almost four-year-old war.
Zelenskiy said on Sunday the Sumy, Kharkiv, Dnipro, Zaporizhzhia, Khmelnytskyi and Odesa regions were targeted in an attack that included more than 200 drones.
The military said 30 strikes had been recorded across 15 locations.
One person was killed in the second-largest city of Kharkiv, said mayor Ihor Terekhov, who in recent days has reported significant damage to local energy facilities as a result of Russian strikes.
It was not immediately clear where the second person had died.
Major cities including the capital Kyiv have faced blackouts and cuts to heating as Russia pounds a power grid already hobbled by a cold snap, leaving residents struggling amid temperatures reaching -16C.
On Saturday, Zelenskiy said he had ordered imports of electricity and additional power equipment to be accelerated as much as possible.
Russia's latest mass attack comes as US and Ukrainian officials meet in Miami to discuss security guarantees and a post-war recovery package for Ukraine.
Washington has pushed Kyiv to agree to a peace framework that it will then present to Moscow, which has been cool on the diplomatic push and has demanded major Ukrainian concessions.
