An apartment building in Kharkiv was hit by a missile overnight, but no casualties have been reported, authorities said.
A rocket strike on a five-storey apartment building in the eastern town of Chasiv Yar on Saturday night killed 15 people and left two dozen people feared trapped in the rubble.
President Volodymyr Zelensky's chief of staff, Andriy Yermak, said the strike was "another terrorist attack" and that Russia should be designated as a state sponsor of terrorism.
Moscow denies it targets civilians, but Ukrainian cities, towns and villages have been left in ruins after Russian shelling, with basements and bomb shelters the only safe place for those who remain.
On Sunday, rescuers in Chasiv Yar used a crane to lift a concrete slab and their hands to dig through the debris, while dazed residents who survived the attack retrieved personal belongings and told stories of their escape.
One woman was seen walking out of the destroyed building carrying an ironing board under her arm, an umbrella and a plastic shopping bag. Others simply watched rescue efforts, fearing the worst as the dead were removed.
"We ran to the basement, there were three hits, the first somewhere in the kitchen," said a resident who gave her name as Ludmila.
"The second, I do not even remember, there was lightning, we ran towards the second entrance and then straight into the basement. We sat there all night until this morning."
Another survivor, who gave her name as Venera, said she had wanted to save her two kittens.
"I was thrown into the bathroom, it was all chaos, I was in shock, all covered in blood," she said, crying. "By the time I left the bathroom, the room was full up of rubble, three floors fell down. I never found the kittens under the rubble."
Russian President Vladimir Putin invaded Ukraine on February 24, calling the conflict a "special military operation" to demilitarise Ukraine and rid it of nationalists.
Ukraine and its Western allies say Putin's war is an imperial land grab and has accused his forces of war crimes. Moscow denies attacking civilians.
The biggest conflict in Europe since World War Two has killed thousands, left cities and towns in ruins and seen more than 5.5 million Ukrainians flee their country.
Ukraine's general staff said on Monday that Russian forces had launched a wave of bombardments in the east as they seek to take control of the Donbas industrial heartland.
It said the widespread shelling was preparations for an intensification of hostilities.
The Kremlin has declared victory in the Donbas' Luhansk province and its troops are now concentrating on seizing control of neighbouring Donetsk.
Putin has promised to hand control of the Donbas to pro-Russian separatists who have declared independence from Kyiv.
Russia abandoned an early advance on the capital Kyiv in the face of fierce resistance bolstered by Western arms.
Ukrainian Deputy Prime Minister Iryna Vereshchuk warned civilians in the Russian-occupied Kherson region on Sunday to urgently evacuate as Ukraine's armed forces were preparing a counter-attack there, not giving a timeframe for action.
"I know for sure that there should not be women and children there, and that they should not become human shields," she said on national television.
Reuters was unable to independently verify the battlefield reports.