The chief of the Russian Wagenr mercenary group, Yevgeny Prigozhin, announced on Saturday from the area confirmed by Reuters to be Bakhmut that the Wagner group had taken full control of the area.
"Today, at noon, at 12 o'clock, Bakhmut has been fully captured," Prigozhin said.
The claim of victory follows fierce fighting last week in which Ukraine said it had pushed back some Russian forces, Reuters reported.
But Ukraine has denied the allegations and said fighting continues in the area where the longest and bloodiest battle in the war, now approaching its 16th month, took place.
Ukrainian military spokesperson Serhiy Cherevatyi told Reuters: "This is not true. Our units are fighting in Bakhmut."
Prigozhin said that his troops would withdraw from Bakhmut again on May 25 for training and hand over control to the Russian regular army.
In the video released by Prigozhin, bombs were heard in the background.
Prigozhin complained, as he has in the past, that the army's forces have suffered much heavier losses than necessary due to inadequate support and ammunition supplies.
Earlier this month, he said that "five times more guys died than should have" due to "whims" of Russia.
British defense intelligence said on Saturday it was "highly likely" that Russia had deployed up to several battalions to reinforce the Bakhmut sector, following Ukrainian tactical gains on the flanks of the town.
It said this represented a "notable commitment by the Russian command."
"Russia's leadership likely continue to see capturing Bakhmut as the key immediate war aim which would allow them to claim some degree of success in the conflict," it said on Twitter.
Prigzohin also mocked Ukrainian President Volodymyr Zelenskyy and US President Joe Biden, who attended the G7 Summit.
After praising the efforts of Ukrainian forces, Prigozhin addressed Zelenskyy and said: "Today when you see Biden, kiss him on the top of his head, say hi to him from me."
Russian President Vladimir Putin congratulated the Wagner mercenary group and Russian soldier for the 'liberation' of Bakhmut.
The Kremlin said the city rescue operation is over.