Russian and Ukrainian forces were engaged in intense fighting on Wednesday over the town of Soledar in eastern Ukraine – a stepping stone in Moscow’s push to capture the entire Donbas region – with the Russians appearing to have the upper hand.

The mercenary group Wagner, which has spearheaded the assault, on Tuesday claimed to have taken control of the small salt-mining town but said pockets of Ukrainian resistance were holding out in the centre.

Russia’s defence ministry said on Wednesday that airborne units had cut off Soledar from the north and south.

But Ukraine’s military denied that Soledar had fallen and said its defensive lines had not been breached. Serhiy Cherevatyi, spokesperson for the eastern military command, told Ukrainian television the intensity of the battles was reminiscent of World War Two.

The Kremlin also stopped short of claiming victory and acknowledged suffering heavy casualties.

“Let’s not rush, let’s wait for official statements. There is a positive dynamic in progress,” Kremlin spokesman Dmitry Peskov said when asked about the situation on the ground.

Reuters was unable to independently verify the situation in Soledar. But a Reuters photographer who has reached the outskirts in recent days said many residents had fled along roads out of the town in perishing cold.

She said plumes of smoke could be seen rising over the town and the incoming artillery fire was relentless.

With the war now in its 11th month, Russian commanders have targeted Soledar as a platform to attack the nearby city of Bakhmut, which has held out for months against a Russian onslaught and is a hub for supply lines in eastern Ukraine.

A victory in Soledar, which had a pre-war population of around 10,000, would have symbolic, military and commercial value for Moscow after battlefield setbacks in recent months.

Ukrainian Deputy Defence Minister Hanna Maliar had said on Tuesday evening that fighting for the town was still raging and the Russians were taking heavy losses in waves of attacks.

“The approaches to our positions are simply strewn with the bodies of dead enemy fighters. Our fighters are bravely holding the defence,” she said.

The Reuters photographer saw ambulances waiting ready to receive the wounded along the road from Soledar to Bakhmut, and chaotic scenes in field hospitals.

The Kremlin’s Peskov acknowledged the high cost of the operation in terms of soldiers’ lives.

“Although tactical successes are also very important, they come at a high price, at the cost of the fantastic heroism of our fighters,” he said.

Soledar was the main item on Russian state television, which rarely mentions Russian reverses in Ukraine. Combative talk show host Olga Skabeyeva called it a “small town with great significance”.

Peskov reiterated previous Kremlin statements that President Vladimir Putin remained open to negotiations, and that Russia would prefer to achieve its goals by political and diplomatic means.

But he said there was no immediate prospect of talks, given the positions of Ukraine and the West. They have dismissed Russian statements on talks as mere propaganda.

The head of the Wagner private militia, Putin ally Yevgeny Prigozhin, had said late on Tuesday that Wagner units had taken control of “the entire territory” of Soledar although fighting was still going on in the town centre.

The Russian state news agency RIA said Wagner had taken over Soledar’s salt mines, and a photograph posted on Wagner’s Telegram channel appeared to show Prigozhin and his fighters inside a mine.

Soledar would be Russia’s most substantial gain since August after a series of retreats in the second half of 2022.

Denis Pushilin, leader of the Russian-controlled part of Donetsk province, said Soledar’s capture would open a prospect of seizing more significant towns further west in what Russia has recognised as the Donetsk People’s Republic – centre of Ukrainian heavy industry and one of four provinces that Russia declared annexed three months ago.

“The opportunity to liberate Artyomovsk [Bakhmut] and Siversk is now multiplied. This is the long-awaited entry to the bridgehead of Kramatorsk, Sloviansk. And this is actually a turning point, now preparations are under way for the moment we have been waiting for – the liberation of the Donetsk People’s Republic.”

Elswhere, the head of the Kherson military administration in southern Ukraine told a news briefing that Russian forces were keeping up their shelling of the provincial capital, which they vacated in November.

Over the previous 24 hours, about 40 infrastructure buildings had been destroyed along with many homes. The children’s hospital was shelled again overnight, he said.

Russia began what it calls a “special military operation” in Ukraine on Feb. 24, saying that Ukraine’s close ties with the West and ambitions to join NATO posed a security threat. Kyiv and its allies accuse Moscow of an unprovoked war to seize territory.

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