The stunt was dismissed by Ukraine, which said its army still holds the embattled eastern city.
The head of Russia’s Wagner mercenary group says he has raised a Russian flag over Bakhmut’s city hall in Ukraine.
In a night-time video, Yevgeny Prigozhin said Bakhmut was now Russian “in a legal sense”.
However he admitted Ukrainian forces were still concentrated in western districts.
Ukraine has insisted its army still holds Bakhmut – an eastern city which Russia has spent months trying to capture.
The General Staff of the Armed Forces of Ukraine said on Sunday evening that while Russia hadn’t stopped its assault on the city, “Ukrainian defenders are courageously holding the city as they repel numerous enemy attacks”.
President Volodymyr Zelensky’s chief of staff, Andriy Yermak, has urged people to “calmly respond to the fakes of those who invent a ‘victory’ that does not exist in reality”.
Ukraine’s Deputy Defence Minister Hanna Maliar said the Wagner claim was “a funny fake”.
In the video, Mr Prigozhin said a tribute to Russian military blogger Vladlen Tatarsky, who died in an explosion at a St Petersburg cafe on Sunday, had been written on the flag.
The BBC has not been able to verify the footage.
Analysis by the Institute for the Study of War said that, as of Sunday, Ukraine still held much of the city – although Russian troops were attempting to envelop it from the south and east.
According to the ISW, the city council building is in part of the city recently claimed by Russia, as it approaches from the east.
Wagner – officially called a private military company – has suffered heavy losses during fighting in Bakhmut.
Many of its recruits are convicts released from Russian prisons drafted in to swell the group’s numbers.
Troops from the regular Russian military are also fighting in Bakhmut, as well as the Wagner troops.
Thousands of Russian and Ukrainian soldiers have died in the fight for control of the city – and it’s thought Russian losses have been far higher than Ukraine’s.
Bakhmut has little strategic value, but Ukraine has seen it as an important drain on Russia’s military equipment and manpower.
Russian commanders hope taking Bakhmut might give them a springboard for further territorial gains.
As the UK Ministry of Defence noted in December, capturing the city “would potentially allow Russia to threaten the larger urban areas of Kramatorsk and Sloviansk”.
Meanwhile, Ukrainian forces are expected to launch a fresh offensive in the coming weeks to try and regain territory that is currently under Russian occupation.
The operation is expected to begin when long-promised Western supplies, including German Leopard tanks, arrive in the country.
Frank Gardner weighs up the possible outcomes for the war, as Ukraine prepares a counter-offensive against Russian forces.
