"Tonight and in the coming hours, it is especially important to pay close attention to air raid warnings," Zelenskiy said in his nightly video address on Saturday.
"The Russians have prepared for a massive attack. Please take care of yourselves."
Russian forces have staged a series of heavy attacks on Kyiv in recent weeks and in other major cities.
Strikes on Monday killed 10 people throughout the country and badly damaged the Pechersk Lavra monastery, a 1000-year-old monastery that stands as a symbol of Ukrainian spiritual and cultural heritage.
Zelenskiy has pledged that his military would press on with its campaign of medium and long-range strikes, focused on the oil sector.
Ukrainian drones struck an oil refinery in Tyumen region in western Siberia on Saturday and Ukrainian drones also struck Moscow's oil refinery twice this week, Zelenskiy said.
Russian forces attacked the southeastern city of Zaporizhzhia with glide bombs on Saturday, killing five people and injuring 10, Regional Governor Ivan Fedorov wrote on Telegram.
He said the city had endured nine strikes and several residential buildings and other infrastructure had been damaged.
Near the Russian border, a bomb attack killed one person on the outskirts of the city of Sumy, local officials said.
In southern Kherson region, regional governor Oleksandr Prokudin said one person had died in a drone attack on a village north of the region's main city, also called Kherson.
Three children were injured when the central city of Poltava came under Russian shelling, local officials said.
Zelenskiy also urged authorities in neighbouring Belarus for the second day running to dismantle relay stations he said were playing a role in staging Russian drone attacks on Ukrainian regions.
Belarus, under longtime President Alexander Lukashenko, has been one of Moscow's closest allies in the more than four-year-old war against Ukraine and allowed the Kremlin to use its territory to launch the February 2022 invasion.
Lukashenko, in power since 1994, has repeatedly said he wants no further involvement in the conflict, but Zelenskiy has urged Belarus to prove that it will not provide direct support for Moscow's war effort.
Zelenskiy did not refer directly to Lukashenko in his nightly video address and alluded to his contested re-election to new terms in office. But he said Ukraine knows of four relay stations in Belarus assisting Russian military activity.
"Belarus still has time to dismantle this equipment. We also know about every factory in Belarus that works for Russia and supports the war," he said.
"Ukraine does not want this and we have warned the de facto leadership of Belarus which has influence over these developments."
On Friday, Zelenskiy said a week should give Lukashenko sufficient time to remove relay equipment from his country and added a threat of Ukrainian action if Lukashenko did not do so.
"If he doesn't do it, we'll do it," Zelenskiy said on Friday, without elaborating.
with DPA
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