This photograph taken on November 29, 2022, shows a destroyed building in Bakhmut, Donetsk region, amid the Russian invasion of Ukraine. AFP
"In the Donetsk area, after offensive actions, Russian troops fully liberated the settlements of Bilogorivka and Pershe Travnya," the defence ministry said a briefing.
Bilogorivka is 25 kilometres (15 miles) north of Bakhmut.
Pershe Travnya -- known as Ozarianyvka in Ukrainian -- is 20 kilometres (12 miles) to the south.
Later on Wednesday the army announced it also seized Andriivka, also to the south.
In another part of the Donetsk region, this time near the city of Avdiivka on the frontline since 2014, Russians seized the small settlement of Vodiane.
The small gains come as Russian forces, desperate for a win after retreating from Kherson in the south and Kharkiv in the north east, have thrown all their might in the battle for Bakhmut.
Once known for its vineyards and cavernous salt mines, Bakhmut has been dubbed "the meat grinder" due to the brutal trench warfare, artillery duels and frontal assaults around the city.
Russian mercenaries, prison conscripts and newly mobilised troops are believed to be fighting for Moscow in the area.
The Ukrainian presidency said Wednesday that gas, electricity and communications were cut off in the city due to shelling.
The Institute for the Study of War said that "Russian forces made marginal gains around Bakhmut on November 29, but Russian forces remain unlikely to have advanced at the tempo that Russian sources claimed."