The head of Russia's Wagner mercenary group has vowed to transfer control of the Ukrainian city of Bakhmut to the Russian army by 1 June.

Wagner founder Yevgeny Prigozhin claimed to have captured Bakhmut on Saturday, but Kyiv says it still controls parts of the city.

Ukraine says its troops are still advancing on the outskirts of Bakhmut.

But Mr Prigozhin said his troops will start handing over the city to the Russian army on Thursday.

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

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

He said that Wagner had set up "defence lines" on the west of the city ahead of the transfer.

But Ukraine's Deputy Defence Minister, Hanna Maliar, reiterated that its forces still have a small foothold inside the city and are advancing on the outskirts, adding that the "intensity" of their movement had reduced.

She later wrote in a post on Telegram that Ukrainian troops still controlled "certain private facilities and the private sector in the 'Litak' area" of the city.

Analysts say 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.

Wagner mercenaries have concentrated their efforts on the city for months and their relentless, costly tactic of sending in waves of men seems to have gradually eroded Kyiv's resistance.

There have been conflicting claims from the two sides over the status of Bakhmut in recent days.

Ukrainian President Volodymyr Zelensky insisted Bakhmut "is not occupied" by Russia, while speaking at the G7 summit in Japan on Sunday.

Russian President Vladimir Putin congratulated Wagner after it said it had captured the city. Mr Prigozhin - posing with some of his fighters - made the claim in a video posted to social media on Saturday.

Mr Prigozhin has staked his reputation, and that of his private army, on seizing the city.

In his latest comments, Mr Prigozhin said: "If the ministry of defence does not have enough personnel, we have thousands of generals."

He has repeatedly targeted top Russian military officials, criticising them publicly for not supporting his troops. Last month, he even threatened to pull his troops out of the city if they were not provided with much-needed ammunition.

The capture of Bakhmut would bring Russia slightly closer to its goal of controlling the whole of Donetsk region, one of four regions in eastern and southern Ukraine annexed by Russia last September following referendums widely condemned outside Russia as a sham.

However, when Russia fought fiercely to claim the cities of Severodonetsk and Lysychansk last summer, Ukraine soon reclaimed swathes of territory elsewhere.

Earlier this month, the US said it believed more than 20,000 Russian soldiers had been killed in the battle for Bakhmut and another 80,000 wounded. The BBC is unable to independently verify the figures.

There were about 70,000 people living in Bakhmut before the invasion, but only a few thousand remain in the devastated city, once best known for its salt and gypsum mines and huge winery.