The Russian announcement on Saturday came hours after Kyiv said the battle was still continuing while admitting the situation was “critical”.
Bakhmut, a salt-mining town that once had a population of 70,000 people, has been the scene of the longest and bloodiest battle in Russia’s 15-month war in Ukraine.
The fall of Bakhmut, where both Russia and Ukraine are believed to have suffered huge losses, would represent Moscow’s first big victory in the conflict in more than 10 months.
“As a result of offensive actions of the Wagner assault units, with the support of artillery and aviation of the ‘Southern’ unit, the liberation of the city of Artemovsk was completed,” Russia’s defence ministry said in a statement, using the Soviet-era name of Bakhmut.
“Vladimir Putin congratulated the assault units of Wagner as well as all servicemen of units of the Russian armed forces who provided them with the necessary support and flank cover, on the completion of the operation to liberate” the city, the TASS state news agency quoted a Kremlin statement as saying.
The Russian president said those who had distinguished themselves would be given awards, the news agency added.
Wagner’s boss Yevgeny Prigozhin earlier claimed the city had fallen to his mercenaries in a video posted on Telegram, in which fighters held Russian flags against a backdrop of ruins.
“Today on May 20, around midday, Bakhmut was taken in its entirety,” Prigozhin said in the video, adding that Wagner fighters would search the captured city before handing it over to the Russian army.
“By May 25 we will completely examine [Bakhmut], create the necessary lines of defence and hand it to the military,” Prigozhin said. “We ourselves will go into field camps.”
Artillery sound could be heard in the background of Prigozhin’s video.
‘Bakhmut will be liberated’
The claims came after a week in which Ukrainian forces have made their most rapid gains for six months on Bakhmut’s northern and southern flanks.
Kyiv had denied Prigozhin’s claim earlier on Saturday but did not have an immediate response to the defence ministry’s statement.
“Heavy fighting in Bakhmut. The situation is critical,” deputy defence minister Hanna Maliar posted on Telegram.
She said Ukrainian troops were “holding the defence” in the city’s “Airplane area”.
“As of now, our defenders control certain industrial and infrastructure facilities in the area,” she said.
It was not possible for Al Jazeera to verify either claim.
Whether the Ukrainian forces have left Bakhmut or not, they have been slowly pulling back inside it, to clusters of buildings on the city’s western edge. Meanwhile, to the north and south, they have seized swathes of territory from Russian troops.
Russia has acknowledged losing some ground around Bakhmut in the past week, while denying assertions by Prigozhin that the flanks around the city guarded by regular troops have collapsed.
Kyiv says its aim in Bakhmut has been to draw Russian forces from elsewhere on the front into the city, to inflict high casualties there and weaken Moscow’s defensive line elsewhere ahead of a planned major counteroffensive.
Moscow has long claimed that capturing Bakhmut would be a stepping stone towards advancing deeper into the Donbas region it claims to have annexed from Ukraine. It has made it the principal target of a massive offensive that failed to capture any significant ground elsewhere.
Prigozhin has acknowledged that Bakhmut has little strategic significance, despite its huge symbolic importance because of the scale of losses in Europe’s bloodiest ground battle since World War II.
The battle for Bakhmut has meanwhile revealed a deepening split between Wagner, a mercenary force that has recruited thousands of convicts from Russian prisons, and the regular Russian military.
For two weeks, Prigozhin has been issuing daily video and audio messages denouncing Russia’s military leadership, often in expletive-laden rants.
In Saturday’s video, he said that because of the “whims” of Defence Minister Sergei Shoigu and Chief of Staff Valery Gerasimov, “five times more guys died than they should have”. He thanked Putin “that he gave us this chance and great honour to defend our motherland”.
Diplomatic blitz
Russia’s announcement that the city had fallen came as Ukrainian President Volodymyr Zelenskyy was set to meet with his American counterpart, Joe Biden, in Japan during the G7 summit.
Biden, who has spearheaded Western backing of Ukraine with sanctions and supplies, “looks forward” to the meeting, a senior official in the United States said, adding that it is expected to take place after 2:00pm local time (0500 GMT) on Sunday.
The Ukrainian president, who was flown in on a French government plane, was able to meet not just G7 leaders but those from other key international players such as unaligned powers Brazil and India.
The fruits of his diplomatic efforts have already paid off, with the US announcing Friday that it would allow Kyiv to acquire F-16 fighter jets, the most sophisticated material yet supplied by the West.
En route to Japan, Zelenskyy also stopped at an Arab League summit in Saudi Arabia.
The Vatican said on Saturday that Pope Francis had asked Cardinal Matteo Zuppi, head of the Italian bishops’ conference, to carry out a peace mission to try to help end the war.