Meanwhile, Pro-Russia separatists said attacks by Ukrainian forces have killed four civilians.
The Ukrainian presidential office said Russian forces targeted cities and villages in the country’s south-east, with most civilian casualties occurring in Donetsk province, where Russia has stepped up its offensive in recent days.
Governor Pavlo Kyrylenko said in a Telegram post that two people died in the city of Avdiivka, which is located in the center of the province, and the Donetsk cities of Sloviansk, Krasnohorivka and Kurakhove each reported one civilian killed.
“Every crime will be punished,” he wrote.
Mr Kyrylenko urged the province’s more than 350,000 remaining residents to flee late on Tuesday, saying that evacuating Donetsk was necessary to save lives and allow the Ukrainian army to put up a better defense against the Russian advance.
Donetsk is part of the Donbas, a mostly Russian-speaking industrial area where Ukraine’s most experienced soldiers are concentrated.
Russian president Vladimir Putin on Monday declared the complete seizure of the region’s other province, Luhansk, after Ukrainian troops withdrew from the last city under their control.
Luhansk governor Serhiy Haidai on Wednesday denied the Russians had completely captured the province.
Heavy fighting continued in villages around Lysychansk, the city Ukrainians soldiers withdrew from and which Russian troops took on Sunday, he said.
“The Russians have paid a high price, but the Luhansk region is not fully captured by the Russian army,” Mr Haidai said.
“Some settlements have been overrun by each side several times already.”
He accused Russian forces of scorched-earth tactics, “burning down and destroying everything on their way”.
Up to 15,000 residents remain in Lysychansk and some 8,000 in the nearby city of Sievierodonetsk, which Russian and separatist fighters seized last month, Mr Haidai said.
Pro-Russian separatists have fought Ukrainian forces and controlled much of the Donbas for eight years.
Before Russia invaded Ukraine on February 24, Mr Putin recognized the independence of the two self-proclaimed separatist republics in the region.
Separatist authorities in Donetsk said on Wednesday that four civilians had been killed and another 14 wounded in Ukrainian shelling over the past 24 hours.
News reports said shelling hit an ammunition depot on Tuesday, triggering massive explosions.
Since Russian forces failed to make inroads in capturing Kyiv, Ukraine’s capital, Moscow has concentrated its offensive on seizing the remaining Ukrainian-held areas of the Donbas.
To the north of Donetsk, Russian forces also hit Kharkiv, Ukraine’s second-largest city, with missile strikes overnight, the Kharkiv regional governor said Wednesday on Telegram.
Three districts of the city were targeted, Governor Oleh Syniehubov said.
Three people, including a toddler, sustained injuries, according to the governor.
A missile struck a building where military registration takes place.