Russian forces have taken control of three Donetsk region towns including Svitlodarsk, regional governor Pavlo Kyrylenko told a local affiliate of Radio Free Europe/Radio Liberty.
Earlier on Tuesday, the Russian-backed Donetsk People's Republic said in a post on the Telegram messaging service that its forces had taken control of the town and replaced the Ukrainian flag with a Russian flag.
Svitlodarsk is 80 kilometers southwest of Sievierodonetsk, the focus of Russian attacks in recent days.
Separately, the self-proclaimed leader of the Moscow-backed separatist region of Donetsk said Tuesday Russian and separatist forces were fighting to take full control of the town of Lyman and have already captured half of it.
"The active phase of the liberation of Krasny Liman is underway," separatist leader Denis Pushilin said on the pro-Kremlin Solovyov Live YouTube programme.
Located in the north of the eastern Donetsk region, Krasny Liman is the old name of the Ukrainian town of Lyman.
Lyman lies on the road to Sloviansk and Kramatorsk, the capital of the Ukrainian-controlled part of the region of Donetsk.
Pushilin said the Russian army and separatist troops have entered the town and controlled around half of it.
"Krasny Liman will also soon be a liberated settlement," he added. "Svyatogorsk will come afterwards and then Slavyansk."
He said Russian and separatist forces have now taken control of 28 settlements in the north of the region of Donetsk.
Svyatogorsk (Svyatogirsk in Ukrainian) and Slavyansk (Sloviansk in Ukrainian) are also located in the region of Donetsk.
There was no immediate comment from Russia and Ukraine. Pushilin's claims could not be independently verified.
Russia is focused on securing and expanding its gains in the eastern Donbas region, near the border and home to pro-Russian separatists, as well as the southern coast.
Separately, the Ukrainian army announced that Russians were now in control of town of Svitlodarsk, also in the Donetsk region.
Regional Governor Pavlo Kyrylenko said on Telegram that Ukrainian troops "have regrouped to take a more favourable position".