Governor Serhiy Gaidai on Sunday said Russian forces dropped a bomb on Saturday afternoon on the school in Bilohorivka where about 90 people were sheltering, causing a fire that engulfed the building.
"The fire was extinguished after nearly four hours, then the rubble was cleared, and, unfortunately, the bodies of two people were found," Gaidai wrote on the Telegram messaging app.
"Thirty people were evacuated from the rubble, seven of whom were injured. Sixty people were likely to have died under the rubble of buildings."
Reuters could not immediately verify the report.
Ukraine and its Western allies have accused Russian forces of targeting civilians in the war, which Moscow denies.
In the ruined southeastern port city of Mariupol, scores of civilians have been evacuated from a sprawling steel plant in a week-long operation brokered by the United Nations and the International Committee of the Red Cross.
Ukrainian President Volodymyr Zelenskiy said in an address late on Saturday that more than 300 civilians had been rescued from the Azovstal steelworks and authorities would now focus on trying to evacuate the wounded and medics. Other Ukrainian sources have cited different figures.
In the Ukrainian-controlled city of Zaporizhzhia, about 230 kilometres northwest of Mariupol, dozens of people who had fled the port city and nearby occupied areas on their own or with the help of volunteers waited to be registered in a car park set up to welcome evacuees.
In an emotional address on Sunday for Victory Day, when Europe commemorates the formal surrender of Germany to the Allies in World War II, Zelenskiy said that evil had returned to Ukraine with the Russian invasion, but his country would prevail.
Russian President Vladimir Putin calls the invasion he launched on February 24 a "special military operation" to disarm Ukraine and rid it of anti-Russian nationalism fomented by the West. Ukraine and its allies say Russia launched an unprovoked war.
Mariupol is key to Moscow's efforts to link the Crimean Peninsula, seized by Russia in 2014, and parts of the eastern regions of Luhansk and Donetsk that have been controlled by Russia-backed separatists since that same year.
Putin sent Victory Day messages to separatist leaders in Luhansk and Donetsk, saying Russia was fighting shoulder to shoulder with them and likening their joint efforts to the war against Nazi Germany. "Victory will be ours," Putin said, according to a Kremlin press release on Sunday.
US President Joe Biden and other G7 leaders were to hold a video call with Zelenskiy on Sunday in a show of unity ahead of Russia's Victory Day celebrations on Monday.
Underlining Western support for Ukraine, Britain pledged to provide a further 1.3 billion pounds ($A2.3 billion) in military support and aid, double its previous spending commitments.
Putin will preside on Monday over a parade in Moscow's Red Square of troops, tanks, rockets and intercontinental ballistic missiles, making a speech that could offer clues on the future of the war.
Russia's efforts have been stymied by logistical and equipment problems and high casualties in the face of fierce resistance.
US Central Intelligence Agency Director William Burns said on Saturday that Putin was convinced "doubling down" on the conflict would improve the outcome for Russia.
"He's in a frame of mind in which he doesn't believe he can afford to lose," Burns told a Financial Times event in Washington on Saturday.
Reuters could not independently verify the claims made by any of the parties to the fighting.
18°C