Ukraine's President Volodymyr Zelensky says that Bakhmut is completely destroyed but has denied that Russia has captured the city.
Asked on Sunday whether his forces had control of the eastern Ukrainian city, Mr Zelensky said: "It's a pity, it's a tragedy, but for today Bakhmut is only in our hearts."
His office later clarified that he had not said that the city had fallen.
The Wagner Russian paramilitary claimed to have captured the city on Saturday.
In a video its founder Yevgeny Prigozhin - posing with some of his fighters - said that his forces had control of the entire city, although Ukraine's government quickly denied that.
Analysts say that Bakhmut is of little strategic value to Moscow, but its capture would be a symbolic victory for Russia after the longest battle of the war in Ukraine so far.
Western officials estimate between 20,000 and 30,000 Russian troops have been killed or wounded in Bakhmut, while Ukraine's military has also paid a heavy price.
Mr Zelensky was asked about Bakhmut at the meeting of G7 nations in Hiroshima, where he has joined key negotiations.
"You have to understand there is nothing," he said.
Hardly a building remains standing in the city, and nearly its entire population has fled.
Mr Zelensky has previously called the city "a fortress" of Ukrainian morale.
Ukraine's hope is that the long-running battle has exhausted Russia's army and supplies.
Wagner forces have led the attack on the city, and Mr Prigozhin has frequently criticised the Russian defence ministry for not providing his fighters with adequate supplies.
In Saturday's video, Mr Prigozhin said: "No-one can pedantically reproach us for the fact that at least some piece was not taken."
He said Wagner troops would pull out of the city later this month to rest, handing control to regular Russian troops.
He has claimed before that his forces had taken Bakhmut, or most of it, only for the battle to continue.
Following Mr Prigozhin's comments, Russian President Vladimir Putin offered his congratulations.
But Ukraine's deputy defence minister rejected the claim while admitting the situation was "critical".
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- 10 May
