Russia's Defence Ministry announced on Friday the capture of three villages in its slow advance across the region.
Ukraine's military did not acknowledge that any of the villages had changed hands.
But it said its forces had recaptured from Russian troops a settlement further west on the edge of Dnipropetrovsk region.
Reuters could not independently confirm battlefield reports from either side.
Since an unsuccessful attempt to advance on the capital Kyiv in the early weeks of the February 2022 invasion of Ukraine, Moscow's troops have focused on seizing the Donbas region in the east, made up of Donetsk and Luhansk regions.
The Russian announcement identified the last two villages to be captured as Kleban-Byk, northwest of the town of Toretsk, which has been under attack for months, and Seredne, closer to the administrative border of northeastern Kharkiv region.
Two of the villages described as captured on Friday -- Katerynivka and Rusyn Yar -- are located near another beleaguered city, Kostiantynivka.
The General Staff of Ukraine's military said only that Katerynivka was one of several localities that came under enemy attack.
A separate military statement said Ukrainian forces had retaken the village of Zelenyi Hai -- adjacent to Dnipropetrovsk region, where Moscow says its forces have made inroads.
The statement said the village was being subjected to new Russian attacks.
Ukraine's military spy agency said it had conducted a joint operation with military units to halt advances in the Donetsk region as well as attempts to break through into Dnipropetrovsk region.
Meanwhile, a fire broke out on the premises of the Kursk Nuclear Power Plant, Russia's federal free-to-air television network REN TV reported early on Sunday.
The fire occurred in a transformer unit that is not part of the nuclear section of the facility, REN TV reported on its Telegram messaging app.
There were no safety threats to people or the plant, the press service told REN TV.
The Wall Street Journal reports The Pentagon has been quietly blocking Ukraine from using US-made long-range Army Tactical Missile Systems to strike targets inside Russia, limiting Kyiv's ability to employ these weapons in its defence against Moscow's invasion
As the White House sought to persuade Russian President Vladimir to join peace talks, an approval process put in place at the Pentagon has kept Ukraine from launching strikes deep into Russian territory, the Journal reported.
Defense Secretary Pete Hegseth has final say over use of the long-range weapons, the Journal said.
Neither Ukraine's presidential office nor the defence ministry immediately responded to Reuters' request for a comment outside business hours. The White House and the Pentagon also did not immediately respond to requests for comment.