But earlier Ukraine's deputy defence minister Hanna Maliar said heavy fighting was ongoing.

She spoke after the head of the Russian private army Wagner had claimed his fighters had completed the capture of the city, after the longest battle of the Ukraine war.

Yevgeny Prigozhin made the claim in a video posted today on the Telegram social messaging service.

He appeared in combat fatigues in front of a line of fighters holding Russian flags and Wagner banners, with ruined buildings in the background and explosions audible in the distance.

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"Today, at 12 noon, Bakhmut was completely taken," Prigozhin said.

"We completely took the whole city, from house to house."

This evening the Russian defence ministry said in a statement: "As a result of offensive actions by Wagner assault units, supported by artillery and aviation of the Southern Group of Forces, the liberation of Artyomovsk has been completed."

Russia refers to the city by its Soviet-era name of Artyomovsk.

Ukraine's deputy defence minister Hanna Maliar said earlier: "The situation is critical."

She added: "As of now, our defenders control certain industrial and infrastructure facilities in this area."

Serhiy Cherevatyi, spokesman for Ukraine's eastern command, also told The Associated Press earlier today that Mr Prigozhin's claim "is not true. Our units are fighting in Bakhmut".

For more than 200 days fighting has raged around Bakhmut, a regional transport and logistics hub in the Donetsk Oblast, part of the largely Russian-speaking industrialised Donbas region which Moscow wants to annex.

Both Russia and Ukraine have endured losses believed to be in the thousands, though neither has disclosed casualty numbers, and it remains unclear which side has suffered there the most.

If Russian forces have taken control of Bakhmut, they would still face the enormous task of seizing the remaining part of the Donetsk region still under Ukrainian control, including several heavily fortified areas.

Ukrainian President Volodymyr Zelenskyy underlined the importance of defending Bakhmut in an interview with The Associated Press in March, saying its fall could allow Russia to garner international support for a deal that may require Kyiv to make unacceptable compromises.

US defence secretary Lloyd Austin and NATO alliance chief Jens Stoltenberg have played down its potential fall as symbolic, as have Western military analysts.

But if Russia has captured Bakhmut, it would bring two bigger cities in the Donetsk region - Kramatorsk and Sloviansk - within easy range of its artillery.

Moscow needs to control both to complete what it calls its "liberation" of the "People's Republic of Donetsk".