Dnipropetrovsk governor Valentyn Reznychenko says three people were killed and seven wounded by shelling in Nikopol when 120 Grad rockets hit the area.
"The enemy is concentrating its efforts on establishing full control over the territories of the Luhansk and Donetsk regions," Ukraine's General Staff said in an early Thursday report, citing more than 60 settlements and military targets.
Heavy fighting raged around the eastern Ukrainian town of Pisky on Thursday, while to the west, Ukraine accused Russian forces of using a nuclear plant to shield artillery.
An official with the Russia-backed Donetsk People's Republic said Pisky, on the front line 10km northwest of the provincial capital Donetsk, was under the control of Russian and separatist forces.
"It's hot in Pisky. The town is ours but there remain scattered pockets of resistance in its north and west," the official, Danil Bezsonov, said on Telegram.
Ukrainian officials denied that the heavily fortified town, a key to the defence of Donetsk, had fallen.
Reuters was unable to verify the battlefield accounts.
The Donbas region, comprised of Luhansk and Donetsk provinces, became Russia's main objective after it failed to seize the capital Kyiv at the beginning of the war in February. Luhansk is now almost completely under Russian control but Donetsk is holding out.
Oleksiy Arestovych, a Ukrainian presidential adviser, said in an interview posted on YouTube that Russian "movement into Pisky" had been "without success".
Luhansk regional Governor Serhiy Gaidai, interviewed on Ukrainian television, said Russia had sent increasing numbers of mercenaries into the region, including from the Wagner private security firm.
"We once had peaceful Ukrainian towns. Now we have been thrust into the Middle Ages ... People are now leaving because they are afraid of freezing in the coming winter," he said.
Ukraine accused Russia on Wednesday of killing at least 13 people and wounding 10 with rockets fired from around a captured nuclear power plant in the centre of the country, in the knowledge it would be risky for Ukrainian forces to return fire.
"The cowardly Russians can't do anything more so they strike towns ignobly hiding at the Zaporizhzhia atomic power station," Andriy Yermak, President Volodymyr Zelenskiy's chief of staff, said on social media.
Ukraine says about 500 Russian troops are at the plant, where Ukrainian technicians continue to work.
The town Ukraine says Russia targeted - Marhanets - is one Russia says its foes have used in the past to shell Russian soldiers at the Zaporizhzhia plant, which they seized in March.
Ukraine's military said Russia also bombarded several other areas in the Zaporizhzhia region. Russia has not commented on the Ukrainian allegations and Reuters could not independently verify Ukraine's account.
