Monday's call to limit power usage comes as the elderly and vulnerable were preparing for a voluntary evacuation of war-ravaged Kherson.
Citizens in the recently liberated southern city, where Kyiv says Russian troops destroyed critical infrastructure before leaving earlier this month, can apply to be relocated to areas where security and heating issues are less acute.
Ukrainians are most likely to live with blackouts - a daily occurrence across the country - at least until the end of March, the head of a major energy provider said.
Russia's response to military setbacks in recent weeks has included a barrage of missile strikes against power facilities that have left millions without electricity as winter sets in and temperatures drop below freezing.
President Volodymyr Zelenskiy has said that half of the country's power capacity had been knocked out by Russian rockets.
In his nightly video address, he urged people to conserve energy, particularly in hard-hit areas such as Kyiv, Vinnytsia in the southwest, Sumy in the north and Odesa on the Black Sea.
"The systematic damage to our energy system from strikes by the Russian terrorists is so considerable that all our people and businesses should be mindful and redistribute their consumption throughout the day," he said.
In a Telegram message for Kherson residents - especially the elderly, women with children and those who are ill or disabled - Deputy Prime Minister Iryna Vereshchuk posted a number of ways residents can express interest in leaving.
"You can be evacuated for the winter period to safer regions of the country," she wrote, citing both security and infrastructure problems.
Kremlin spokesman Dmitry Peskov said the blackouts and Russia's strikes on energy infrastructure are the consequences of Kyiv being unwilling to negotiate.
Battles continued to rage in the east following Russian troop movements into the industrial Donbas region from around Kherson in the south.
Ukraine's military said on Monday Russian forces had tried to make advances around Bakhmut and Avdiivka in Donetsk, and bombarded nearby towns.
Moscow has been reinforcing the areas it still holds and pressing an offensive of its own along a stretch of front line west of the city of Donetsk held by its proxies since 2014.
Russia and Ukraine have traded blame for at least a dozen explosions at Ukraine's Zaporizhzhia nuclear power station, which has been under Russian control since soon after it invaded the country on February 24.
Ukraine narrowly escaped disaster during fighting at the weekend that rocked the plant, Europe's largest, with a barrage of shells.
Some fell near reactors and damaged a radioactive waste storage building, the United Nations nuclear watchdog said.
Zelenskiy urged NATO members to guarantee protection from "Russian sabotage" at nuclear facilities.
The head of Russia's state-run nuclear energy agency, Rosatom, said it had discussed Sunday's shelling with the IAEA, and said there was a risk of a nuclear accident.
IAEA experts toured the site on Monday, and the agency said they found widespread damage but nothing that compromised the plant's essential systems.
The reactors are shut down but there is a risk that nuclear fuel could overheat if the power driving the cooling systems is cut.
Shelling has repeatedly cut power lines.
Russia's defence ministry said Ukraine fired at power lines supplying the plant.
Ukraine's nuclear energy firm Energoatom said Russia's military shelled the site, accusing it of nuclear blackmail and actions that were "endangering the whole world".
Reuters could not immediately verify which side was responsible.
Repeated shelling of the plant during the war has raised concern about a grave disaster in the country that suffered the world's worst nuclear accident, the 1986 Chernobyl meltdown.
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