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Ukraine on Monday said it continued to fight for Bakhmut and still controlled a corner of the eastern city, as Russia's Wagner said it would transfer control of the ruined hotspot to the Russian army by June 1.

Ukraine has denied that Bakhmut has fallen to Russian forces, saying it is hanging on to one area of the city and that battles are ongoing.

Both Wagner and the regular Russian army said over the weekend that Bakhmut has fallen to them.

"The fighting continues," Ukraine's deputy defence minister Ganna Malyar said, a day after President Volodymyr Zelensky said Bakhmut was "not occupied" by Russia.

Malyar said Kyiv's troops retained control of the "Airplane" district of Bakhmut.

"The battle for the dominant heights on the flanks -- north and south of the suburbs -- continues," she added.

The head of Russia's mercenary group Wagner, whose fighters have spearheaded Moscow's storming of Bakhmut, announced on Saturday that the city had fully fallen to his fighters.

On Monday, he said the mercenaries would leave Bakhmut by June 1 and hand over control to regular Russian troops.

"Wagner will leave Artemovsk from May 25 to June 1," Yevgeny Prigozhin said in an audio recording on Telegram.

Bakhmut was previously known as Artemovsk, in honour of a Soviet revolutionary, before Ukraine renamed it.

Prigozhin said the mercenaries had set up "defence lines" on the western outskirts of the city before a planned transfer of control to the Russian army.

"If the ministry of defence does not have enough personnel, we have thousands of generals," said Prigozhin, who has been embroiled in an increasingly public spat with the Russian military leadership.

Prigozhin has poured scathing criticism on Russian Defence Minister Sergei Shoigu and army chief of staff Valery Gerasimov, accusing them of being incompetent and causing Moscow's large-scale losses in the conflict in Ukraine.

Prigozhin's influence has risen hugely during Moscow's Ukraine offensive.

He had previously said Wagner fighters would pull out by May 25.

Russian President Vladimir Putin congratulated Wagner and the Russian army on the alleged conquest.

But Zelensky said at the G7 summit on Sunday that Bakhmut was "not occupied" by Russia.

Both sides are believed to have suffered huge losses in the battle for Bakhmut, the longest and bloodiest in Moscow's offensive.

Bakhmut, a salt-mining city in the Donetsk region, had a pre-war population of around 70,000 people.

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