In his nightly video address, Ukraine's president said his fellow countrymen must not allow Moscow to "spread despondency and fear" as they mark the 31st anniversary of independence from Soviet rule.
"We must all be aware that this week Russia could try to do something particularly ugly, something particularly vicious," Zelenskiy said ahead of the anniversary on August 24, which also marks six months since Russia's full-scale invasion of Ukraine began.
The curfew in Ukraine's second largest city, Kharkiv, would be extended for the entire day on August 24, regional governor Oleh Synehub said.
The northeastern city is regularly hit by Russian shelling and normally has a curfew from 10pm to 6am.
Also on Saturday, a Russian missile hit a residential area of a southern Ukrainian town not far from a nuclear power station, wounding 12 civilians.
That strike at the Pivdennoukrainsk (South Ukraine) nuclear station and fresh shelling near the Zaporizhzhia plant, Europe's largest such facility, prompted new fears of a nuclear accident during the war, Ukrainian officials said.
Zelenskiy in his address also referred obliquely to a series of explosions in recent days in Crimea, the Ukrainian territory seized and annexed by Russia during a 2014 incursion.
Ukraine has not claimed responsibility for the attacks, but analysts have said some have been made possible by new equipment used by Ukrainian forces.
"You can literally feel Crimea in the air this year, that the occupation there is only temporary and that Ukraine is coming back," Zelenskiy said.
In the latest attack in Crimea, the Russian-appointed governor not recognised by the West said a drone had struck a building near the headquarters of Russia's Black Sea Fleet on Saturday morning.
"A drone flew onto the roof. It was flying low," governor Mikhail Razvozhayev said on Telegram.
"It was downed right over the Fleet headquarters. It fell on the roof and burned up. The attack failed."
Ukrainian media reported explosions in nearby towns - including the resorts of Yevpatoriya, Olenivka and Zaozyornoye.
Following the strike near the South Ukraine power station, Vitaliy Kim, governor of Mykolaiv region, said on Telegram that four children were among the wounded.
Private homes and a five-storey apartment block were damaged in Voznesensk, 30km from the plant, Ukraine's second largest.
The general prosecutor's office in Mykolaiv region, updating an earlier toll, said 12 civilians had been wounded.
State-run Energoatom, which manages all four Ukrainian nuclear energy generators, described the attack on Voznesensk as "another act of Russian nuclear terrorism".
"It is possible that this missile was aimed specifically at the Pivdennoukrainsk Nuclear Power Plant, which the Russian military tried to seize back at the beginning of March," Energoatom said in a statement.
Russia did not immediately respond to the accusation and Reuters was unable to verify the situation in Voznesensk.
There were no reports of any damage to the South Ukraine plant.
Meanwhile, Russia and Ukraine traded fresh accusations of shelling around the Zaporizhzhia station, held by Russia since March.
Vladimir Rogov, a Russia-appointed official in the nearby town of Enerhodar, said Ukrainian forces had launched at least four strikes on the plant.
Yevhen Yetushenko, mayor of Ukrainian-controlled Nikopol on the opposite bank of the Dnipro River, said Russian forces had repeatedly shelled the town.
Talks have been underway for more than a week to arrange for a visit to the plant by the UN nuclear power agency, the International Atomic Energy Agency.
Ukrainian authorities have called on the United Nations and other international organisations to compel Russian forces to leave the Zaporizhzhia plant.
And in Mariupol, a town in eastern Ukraine controlled by Russia after weeks of shelling, officials said the new Russian-appointed mayor, Konstantin Ivashchenko, had survived an assassination attempt.
"It didn't work," Petro Andryushchenko, an official of the ousted city council, said on Telegram.
"But this is only the beginning."
