The regional emergency service gave the latest death toll from the strike in the town of Chasiv Yar as 10 people, with rescue work still going on.
Donetsk region Governor Pavlo Kyrylenko said on Telegram that at least 34 people could be trapped under the ruins.
Andriy Yermak, chief of staff to Ukraine’s president, said in a Telegram post that the strike was "another terrorist attack," and that Russia should be designated as a "state sponsor of terrorism" as a result.
Russia, which says it is conducting a "special military operation" to demilitarise Ukraine, denies targeting civilians.
Meanwhile, Luhansk Governor Serhiy Gaidai said on Telegram that Russian forces were gathering in the area of the village of Bilohorivka, about 50 km (30 miles) east of Sloviansk, from where they were shelling the surrounding settlements and carrying out air strikes.
Russia’s Tass news agency cited pro-Russian separatists as saying Ukrainian forces had fired an artillery barrage into residential districts of the city of Donetsk.
Reuters could not independently verify battlefield accounts.
Russian forces have likely made further territorial advances around Popasna, in Ukraine’s Luhansk Oblast, British defence intelligence said on Sunday.
Latest Defence Intelligence update on the situation in Ukraine - 10 July 2022
Find out more about the UK government's response: https://t.co/0wJwGgHXit
🇺🇦 #StandWithUkraine 🇺🇦 pic.twitter.com/T0mS7E9OIG
— Ministry of Defence 🇬🇧 (@DefenceHQ) July 10, 2022
Russian artillery continues to strike in the Sloviansk area of the Donbas region from around Izium to the north, and near Lysychansk to the east, a Ministry of Defence update said.
Fires from Izium continue to focus along the axis of the E40 main road, intelligence said, a key road which links Donetsk to Kharkiv.
The road is likely to be an important objective for Russia as it attempts to advance through Donetsk Oblast, British authorities said.