Ukrainian officials said Russian shelling killed another four people in the eastern Donetsk region on Monday, while a man and a woman were killed in Kharkiv, in the northeast, when shells hit a playground near a residential building.
Ukrainian President Volodymyr Zelenskiy said Russian forces had begun the "Battle of Donbas" after senior officials said Moscow had begun a new offensive push along most of Ukraine's eastern flank.
"A very large part of the entire Russian army is now focused on this offensive," Zelenskiy said in a video address, adding: "No matter how many Russian troops they send there, we will fight. We will defend ourselves."
Ukrainian media reported a series of explosions, some powerful, along the front line in the Donetsk region, with shelling taking place in Marinka, Slavyansk and Kramatorsk. Ukrainian officials and local media also said further explosions were heard in Kharkiv, Mykolaiv in the south and Zaporizhzhia in the southeast.
Reuters was not immediately able to verify the reports.
The mayor of Lviv, Andriy Sadoviy, said the blast also wounded 11 and shattered windows of a hotel housing evacuees from elsewhere in the country.
"Seven peaceful people had plans for life, but today their life stopped," he said.
Driven back by Ukrainian resistance in the north, Moscow has refocused its ground offensive in the two eastern provinces known as the Donbas, while launching long-distance strikes at other targets including the capital, Kyiv.
The regional governor of Kharkiv said authorities were continuing to evacuate people from two areas where they expect fighting to take place.
Russia's defence ministry said it had hit hundreds of military targets in Ukraine overnight. It said air-launched missiles had destroyed 16 military facilities across Ukraine.
It added that the Russian air force had launched strikes against 108 areas where Ukrainian forces were concentrated and Russian artillery struck 315 Ukrainian military targets.
Western capitals and Kyiv accuse Russian President Vladimir Putin of unprovoked aggression.
Russia denies targeting civilians in what it calls a special operation to demilitarise Ukraine and eradicate dangerous nationalists. It rejects what Ukraine says is evidence of atrocities, saying Ukraine has staged them to undermine peace talks.
Russia has been trying to take full control of the southeastern port city of Mariupol, which has been besieged for weeks and which would be a huge strategic prize, linking territory held by pro-Russian separatists in the east with the Crimea region that Moscow annexed in 2014.
No fewer than 1000 civilians were hiding in underground shelters beneath the vast Azovstal steel plant, the city council said on Monday.
Video and audio footage showed explosions rumbling and smoke rising from the steelworks, which contain myriad buildings, blast furnaces and rail tracks.
Russia's invasion has damaged or destroyed up to 30 per cent of Ukraine's infrastructure at a cost of $US100 billion ($A136 billion), a Ukrainian minister said, adding reconstruction could be achieved in two years using frozen Russian assets to help finance it.
The United Nations on Monday said the civilian death toll from the war had reached 2072 as of midnight on April 17 from the start of the Russian invasion on February 24.
About four million Ukrainians have fled the country.