Ukraine's atomic energy agency accused Russia of using Europe's largest nuclear power plant to store weapons and shell the surrounding regions of Nikopol and Dnipro that were hit on Saturday.
Petro Kotin, president of Ukrainian nuclear agency Energoatom, called the situation at the Zaporizhzhia nuclear plant "extremely tense" with up to 500 Russian soldiers controlling the plant.
The plant in southeast Ukraine has been under Russian control since the early weeks of Moscow's invasion, though it is still operated by Ukrainian staff.
"The occupiers bring their machinery there, including missile systems, from which they already shell the other side of the river Dnipro and the territory of Nikopol," he said in a Ukrainian television interview broadcast on Friday.
On Saturday, Russian missiles struck residential buildings in the city of Nikopol, killing two people, Dnipro regional governor Valentin Reznichenko said.
In the northeast region around Ukraine's second city of Kharkiv, governor Oleg Synegubov said an overnight Russian missile attack killed three people in the town of Chuguiv.
In the central Ukrainian city of Vinnytsia, officials said the death toll rose to 24 from Russian strikes after a woman died of her injuries in hospital on Saturday. Ukraine says three children are among the dead.
"Sixty-eight people continue treatment, including four children. Four people are still missing," said Vinnytsia district chief Sergiy Borzov.
- Outpouring for 4-year-old -
President Volodymyr Zelensky accused the Russians of aiming to "cause maximum damage to Ukrainian cities".
"I'm urging you, once again: please don't ignore the air raid signals now," he said in his daily address on Friday.
Russia claimed the strikes in Vinnytsia -- hundreds of kilometres away from frontline fighting -- had killed Ukrainian military officials and foreign arms suppliers.
But Ukraine said the dead included four-year-old Liza Dmitrieva, who had Down's syndrome and whose death spurred an outpouring after footage of her final moments alive went viral on social media.
Officials initially believed Liza's mother was also killed, but have since confirmed she is in a "critical" condition after surgery.
The missile strikes on Vinnytsia were the latest attacks to carry a heavy civilian toll and came less than a week after strikes on Chasiv Yar in the Donetsk region left nearly 50 dead.
"I have no words to describe the horror I experienced today," said Anastasiya, after rockets fell near her home in Kramatorsk, a major city and an administrative centre of the Donbas, on Friday.
"It's good that it fell outside and did not fly into the house. That was lucky."
- 'Clearing' Donbas town -
Moscow invaded Ukraine on February 24 and the conflict has killed thousands of people, destroyed cities and forced millions to flee their homes.
The heaviest fighting has recently focused on the industrial Donbas region in the east, where grinding trench battles and artillery duels are morphing into a war of attrition.
Britain said Friday that the Kremlin "must bear the full responsibility" for the death of a British captive in east Ukraine.
"I am shocked to hear reports of the death of British aid worker Paul Urey while in the custody of a Russian proxy in Ukraine," Foreign Secretary Liz Truss said.
Moscow-backed separatists said Friday they were closing in on their next target, Siversk, after wresting control of sister cities Lysychansk and Severodonetsk about 30 kilometres (18 miles) to its east.
And Donetsk separatist official Daniil Versonov said rebel fighters were "clearing" eastern districts of Siversk in small groups.
Ukraine has repeatedly urged allies to supply it with advanced, long-range precision artillery systems that would allow it to target Russian forces deeper inside Ukrainian-held territory.
Defence Minister Oleksiy Reznikov said Friday that Ukraine had taken delivery of its first batch of sophisticated M270 rocket systems, adding to a growing arsenal of Western-supplied artillery Kyiv says is changing dynamics on the battlefield.