A ministry report said the villages of Zolota Nyva and Zoryane Pershe had been brought under Russian control. The communities have an estimated population of a few hundred residents each.
The two villages lie to the north and south of Kurakhove, one of the focal points of military activity on the eastern front.
Official Ukrainian accounts of the fighting did not mention the loss of control of either village. But the Ukrainian General Staff acknowledged that the Kurakhove sector was the scene of the heaviest battles on the eastern front.
The General Staff last referred to Zolota Nyva on Sunday as one of two villages coming under a series of Russian assaults.
Ukrainian forces last week abandoned the hilltop town of Vuhledar, farther south, after two years of successfully defending against successive Russian attempts to capture it.
A spokeswoman for the Ukrainian military said on Monday that Russian forces had entered the outskirts of the eastern Ukrainian frontline city of Toretsk, to the northeast of Kurakhove.
Russian media quoted an adviser to the Russia-installed administration of the Donetsk region, Igor Kimakovsky, as saying Russian troops had made their way into the center of town from different directions. They now controlled all high-rise residential buildings.
Ukrainian military bloggers said Russian troops had taken control of the town center and were encountering resistance while trying to take over northeastern districts.
But they acknowledged that Russian forces “held the initiative” in the area.