The head of the Russian Wagner mercenary group claimed on Wednesday that his soldiers had fully gained control of Bakhmut, a city in eastern Ukraine. According to the secretary general of NATO, the entire city may soon come under the hands of the invading army.

If Yevgeny Prigozhin, the head of Wagner, is correct, Russian forces now hold about half of the city in their expensive campaign to win their first significant victory in several months.

But as one of the bloodiest battles of the year-long war ground on amid the ruins, Ukrainian defenders remained defiant.

Last week they appeared to be preparing for a tactical retreat from Bakhmut, but Ukrainian military and political leaders now speak of hanging on to positions and inflicting as many casualties as possible on the Russians.

The General Staff of Ukraine’s armed forces said in its Wednesday morning report: “The enemy, despite significant losses, continues to storm the town of Bakhmut.”

Prigozhin said his fighters, who have been spearheading the Russian assault on Bakhmut, had now captured the city’s east.

“Everything east of the Bakhmutka River is completely under the control of Wagner,” Prigozhin said on Telegram.

The river bisects Bakhmut, which sits on the edge of a swathe of Donetsk province that is already largely under Russian occupation. The city center is on the west side of the river.

Prigozhin has issued premature success claims before and Reuters was not able to verify his latest one.

But in Stockholm, NATO Secretary-General Jens Stoltenberg struck a pessimistic note. Speaking before an European Union defence ministers’ meeting, he said Russia was throwing more troops into the battle.

“They have suffered big losses, but at the same time we cannot rule out that Bakhmut may eventually fall in the coming days,” Stoltenberg said.

This would not necessarily be a turning point in the war, he added, but it showed “we should not underestimate Russia, we must continue to provide support to Ukraine”.

The Ukrainian military said earlier the main task of its troops in Bakhmut was to cause as many casualties as possible among the Russians and grind down their fighting capability.