Russian mercenary leader Yevgeny Prigozhin said forces of his Wagner group had captured the village of Yahidne, just north of Bakhmut in eastern Ukraine on Saturday.
But Ukrainian military reports issued a day after the first anniversary of Russia's invasion of Ukraine, suggested that villages near the key town remained under Kyiv's control.
Reuters could not independently confirm Prigozhin's claim, in a short audio message, or the report by the Ukrainian military's general staff.
"At 1900 on 25th February, storm units of the Wagner private military company secured complete control of the locality of Yagodnoye (Yahidne) to the north of Bakhmut," Prigozhin said in the audio clip.
A day earlier, he said Wagner had taken control of Berkhivka, an adjacent village on the outskirts of Bakhmut.
The months-long struggle for Bakhmut, where only about 5,000 of 70,000 residents remain, has seen some of the bloodiest attritional fighting of Russia's invasion.
Wagner units have suffered heavy losses, prompting Prigozhin to complain bitterly that the Russian defence establishment has failed to properly acknowledge their contribution.
This week he even accused the army top brass of treason for failing to supply his men with sufficient ammunition, though he later said the situation had been remedied.
The prolonged siege has prompted Ukrainian analysts to consider openly whether its troops should consider abandoning their defence of the city.
On Thursday, Ukrainian military analyst Oleh Zhdanov acknowledged in a YouTube presentation that Berkhivka had come under Russian control.
The latest general staff report said Russian forces had made unsuccessful advances on villages around Bakhmut, including Berkhivka.
There was no mention in the report of Yahidne. But it said 18 localities in the area had been shelled by Russian forces, including villages on Bakhmut's southern and western approaches.
(Reporting by Mark Trevelyan and Ron PopeskiEditing by Frances Kerry and Sandra Maler)