KYIV (Reuters) -Ukraine said on Sunday that its forces were still advancing around the edges of Bakhmut, aiming to encircle the ruined eastern city after Moscow congratulated the Wagner private army and Russian troops for capturing it.

Russia said on Saturday it had completely taken Bakhmut, which, if confirmed, would mark an end to the longest and bloodiest battle of the 15-month war. Russian President Vladimir Putin praised his regular troops and the Wagner group.

On Sunday, however, a top Ukrainian general said Kyiv's forces still controlled what he accepted was an "insignificant" part of Bakhmut, although that would allow them to enter the city when the situation changed.

General Oleksandr Syrskyi said in a Telegram post that Kyiv's troops were advancing on Russian forces in the suburbs and getting closer to a "tactical encirclement" of the city, formerly home to 70,000 people.

Syrskyi, the commander of Ukraine's ground forces, said on Sunday he had visited front-line positions near Bakhmut, where fighting has raged for more than nine months. Syrskyi's assertion that Ukrainian forces were continuing their advance along the flanks of the city was echoed by Ukraine's Deputy Defence Minister Hanna Maliar.

"Our forces have taken the city in a semi-encirclement, which gives us the opportunity to destroy the enemy ... the enemy has to defend himself in the part of the city he controls," Maliar said on Telegram.

Ukrainian troops were still defending industrial and infrastructure facilities and had claimed part of the overlooking heights, Maliar said.

In the past 24 hours, the Russian offensive around Bakhmut has not let up, including air strikes on the city and the village of Ivanivske on its western approaches, said a statement by the General Staff of the Ukrainian Armed Forces.

Later on Sunday, Wagner leader Yevgeny Prigozhin said in an audio message on Telegram that his group's job was done and his forces would leave the conflict zone within days.

"Wagner today captured no territory. We have captured all the territory we promised to capture, right up to the last centimetre," Prigozhin said. "As we stated yesterday. We are handing over our positions to (Russia's) Defence Ministry and on the 25th (of May) we are leaving the conflict zone."

Bakhmut has no strategic value according to military analysts, although Moscow has said that capturing it would be a stepping stone towards advancing deeper into the industrial region of Donbas it claims to have annexed from Ukraine.

Reuters could not verify the battlefield reports by either side.

ZELENSKIY COMPARES BAKHMUT TO 'RUINED HIROSHIMA'

Over the past week, Ukrainian forces have made their most rapid gains for six months on Bakhmut's northern and southern flanks, with Russia acknowledging some setbacks for its troops.

Kyiv says its aim 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 Ukrainian counteroffensive.

U.S. President Joe Biden said Russia had suffered more than 100,000 casualties in Bakhmut, the destruction of which Ukrainian President Volodymyr Zelenskiy compared to the U.S. World War Two atomic bomb attack on Hiroshima, in Japan.

"I'll tell you openly: Photographs of ruined Hiroshima absolutely remind me of Bakhmut and other similar settlements. Nothing left alive, all the buildings ruined," he said as he attended a Group of Seven summit in the Japanese city on Sunday.

"Bakhmut has not been captured by the Russian Federation as of today. There are no two or three interpretations of this," he told reporters.

In his nightly video address, on Sunday aboard an aircraft, Zelenskiy said: "The world hears our position. Defence, security guarantees, the recovery of all our territories and all our people, justice, the implementation of our peace plan." 

Taking Bakhmut - which Russia refers to by its Soviet-era name of Artyomovsk - would represent Moscow's first big victory in the conflict in more than 10 months.

The battle for Bakhmut has shown a deepening split between Wagner, which 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.

Leaders of the world's richest democracies at the G7 summit said they would not back down from supporting Ukraine.

Zelenskiy, who held a private meeting with Biden in Hiroshima, said he was confident Kyiv would receive F-16 fighter jets from the West after months of lobbying for the planes.

Biden said F-16s would not have helped Ukrainian forces with regard to Bakhmut but could "make a big difference in terms of being able to deal with what is coming down the road".