The announcement came after Ukrainian President Volodymyr Zelensky warned that if Bakhmut fell, Moscow would gain an "open road" for offensives deeper into the country.

Wagner chief and Kremlin ally Yevgeny Prigozhin said on social media that his forces "have taken all of the eastern part of Bakhmut", a salt-mining town with a pre-war population of 80,000.

The intense fighting around Bakhmut has been the longest and bloodiest in Russia's more than year-long invasion, which has devastated swathes of Ukraine and displaced millions of people.

Both sides have said the Bakhmut battle has cost a significant number of troops, though neither has given figures.

Ukrainian officials say around 4,000 civilians remain in the town, which has been virtually flattened, including dozens of children.

Zelensky warned in an interview with CNN what could happen if Bakhmut falls to Russian forces.

"We understand that after Bakhmut, (Russian forces) could go further" and attack nearby cities in the Donetsk region.

"They could go to Kramatorsk, they could go to Sloviansk, it would be an open road for the Russians after Bakhmut to other towns in Ukraine, in the Donetsk direction," Zelensky said in an interview set to air Wednesday.

Wagner has spearheaded the attack on Bakhmut and its chief, Prigozhin, is locked in a dispute with Russia's military leadership.