Footage on social media shows Ukrainian troops celebrating in Blahodatne and Neskuchne – presumably meaning they have regained control of the small villages.
Kyiv Deputy Defense Minister Hannah Maliar said nearby Makarivka was also taken.
This comes after Russia announced yesterday that it wants to regain control of the Wagner Group after months of power struggles.
Photos released online show soldiers looking out the windows of a building they appear to have taken control of.
Other footage shared by pro-Ukrainian reports showed troops raising the Ukrainian flag in front of a burned-out building in Blahodatne.
And the state border guard released videos in which Kiev’s forces announced that “Neskuchne of the Donetsk region is back under the Ukrainian flag,” before shouting the now-standard rallying cry of “Glory to Ukraine.”
While the capture of the three villages represents the biggest advance of the past few days, the settlements are relatively small.
Deputy Defense Minister Hanna Maliar claimed in a Telegram video that Ukraine’s armed forces also took the village of Makarivka.
An army spokesman said the successes were the first local victories of the counteroffensive.
While the capture of the three villages represents the biggest advance of the past few days, the settlements are relatively small. Blahodatne had a population of just 1,000 before the war.
The village, which has been the focus of fierce fighting in recent days, lies on the road towards the city of Mariupol, and some analysts suspect Ukraine could try to retake the port city in the coming months.
Others have speculated that Kiev wants to breach the land bridge between occupied Crimea and Donetsk, thereby isolating Russian troops on the peninsula.
Further east, Ukrainian troops are also said to have advanced near the devastated town of Bakhmut, which was the scene of a long and bloody battle between Ukrainian forces and Russian troops.
Those three settlements would be the first to be liberated since his comments, but not the first Ukraine has retaken since Monday when parts of its forces began advancing in the south of the country.
Moscow has not yet confirmed the fall of one of the villages, instead speaking of repelling Ukrainian attacks in the region.
Elsewhere, Ukraine reports that Russia blew up another dam in the Zaporizhia region after destroying the large Kakhovka dam on Monday.
This led to widespread flooding and mass evacuations. President Zelenskyy said on Sunday that 4,000 people had been evacuated.
Ukraine says the dam was blown up by Russian forces, who have controlled it since February 2022.
Valeriy Shershen, a spokesman for Ukraine’s military, said Moscow forces decided to blow up a second dam near the village of Novodarivka, which “resulted in flooding on both banks of the Mokri Yaly River.”
Mr Shershen said Russia was deliberately blowing up dams in the region to halt Ukraine’s advance towards the occupied territories.
Russia has denied blowing up the Kakhovka Dam, instead blaming Ukraine.
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