Russia on Monday opened fire with artillery, multiple rocket launchers and tanks around Ukraine's second largest city Kharkiv and shelled cities in the east, Ukraine's general staff said, following a strike that killed 18 people in an apartment building.

The rocket strike on the five-storey residental block in Chasiv Yar on Saturday night also left two dozen people trapped in the rubble, the emergency service said. Rescuers were in voice contact with two people under the wreckage, it said.

The rocket attack was part of Russia's push to capture all of Donetsk province, which makes up part of the industrial Donbass region in the east along with Luhansk province, where Moscow declared victory earlier this month.

Ukrainian President Volodymyr Zelenskyy said Russia had carried out 34 airstrikes since Saturday, while his chief of staff, Andriy Yermak, said Moscow should be designated as a state sponsor of terrorism for the apartment bombing.

In a separate incident, an apartment block in Kharkiv, in the northeast but outside the Donbass, was struck by a missile overnight, but no casualties have been reported, authorities said, adding that a school was also hit.

Moscow denies targeting civilians, but Ukrainian cities, towns and villages have been left in ruins after Russian shelling since the Feb. 24 invasion, with basements and bomb shelters the only safe place for those who remain.

On Sunday, rescuers in Chasiv Yar deployed a crane to lift a concrete slab and used 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 calls the conflict a "special military operation" to demilitarize neighboring Ukraine and rid it of nationalists. Ukraine and its Western allies say Putin's war is an imperial-style land grab and has accused his forces of war crimes.

The biggest conflict in Europe since World War II has killed thousands of people, left cities and towns in ruins and seen more than 5.5 million Ukrainians flee their country.

Wave of bombardments

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 all of the Donbass, a region partly controlled by Russian-backed separatists since 2014.

It said the widespread shelling amounted to preparations for an intensification of hostilities.

After taking Luhansk province, Russian forces are now concentrating on seizing control of Donetsk to the south.

On Monday, Tass news agency cited separatist officials and a source in Luhansk saying Russian and Russian-backed forces had taken control of three villages in Donetsk province.

Russia abandoned an early advance on the capital Kyiv in the face of fierce resistance bolstered by Western weapons.

Ukrainian Deputy Prime Minister Iryna Vereshchuk warned civilians in the Russian-occupied Kherson region in the south on Sunday to urgently evacuate as Kyiv's forces were preparing a counterattack there. She gave no 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.