The head of Russia's Wagner mercenary group said on Wednesday (local time) his forces had taken full control of the eastern part of the Ukrainian city of Bakhmut and NATO'S secretary general said it could all fall to the invading army in the next few days.

If Wagner boss Yevgeny Prigozhin's claim is true, it would mean Russian forces now control nearly half the city in their costly push to secure their first big 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 centre 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.

DEVASTATED CITIES

Russia, which claims to have annexed nearly 20% of Ukraine's territory, says that taking Bakhmut would be a step towards seizing the whole of the eastern industrial Donbas region, made up of Donetsk and Luhansk provinces.

Western analysts say Bakhmut has little strategic value although its capture would be a boost to President Vladimir Putin and his military after a series of setbacks in what they call their "special military operation" in Ukraine.

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Kyiv says the losses suffered by Russia there could determine the course of the war, with decisive battles expected when the weather improves and Ukraine receives more Western military aid, including heavy battle tanks.

The months of warfare in the east have been among the deadliest and most destructive since Russia invaded in February last year, adding Bakhmut's name to a list of devastated cities such as Mariupol, Sievierodonetsk and Lysychansk.

A Ukrainian military drone showed the scale of destruction in Bakhmut, filming apartment blocks on fire and smoke billowing from residential areas.

Iryna Vereshchuk, a deputy Ukrainian premier, said fewer than 4,000 civilians - including 38 children - out of a pre-war population of some 70,000 remained in the city, now largely in ruins after months of bombardment.

"The situation in the city is difficult. The enemy actively storms our positions. However, they don't have any success and suffer colossal losses," a Ukrainian border guard said in a video released by the State Border Service.

"The city stands, because Bakhmut was, is, and will be Ukraine."

Luhansk Governor Serhiy Haidai said Russia's strategy in eastern Ukraine was to take the remaining areas of Donetsk and Luhansk that it does not control.

"As for tactics - they understand that they are not able to make any rapid advance, so they have one tactic - they advance where they can. If they see that there is any success somewhere, they throw all the reserves into it," he told Ukrainian TV.

MORE SHELLS

In Stockholm, EU defence ministers were meeting to discuss further arms supplies to Kyiv. Shipments of battle tanks and artillery are already in the pipeline but it could take months before they can be put into action on the front lines.

Ukrainian Defence Minister Oleksii Reznikov said Kyiv urgently needed huge supplies of artillery shells to mount a general counter-offensive against Russia's army.

He urged EU members to support an Estonian plan for joint procurement of munitions.

Ukraine is burning through shells faster than its allies can manufacture them and Reznikov said Kyiv wanted 90,000-100,000 artillery rounds per month.

He said he supported a proposal by Estonia for EU countries to club together to buy 1 million 155-millimetre shells for Ukraine this year at a cost of 4 billion euros ($4.22 billion).

"We need to move forward as soon as possible," Reznikov told reporters before the meeting.

German Defence Minister Boris Pistorius said it would take time for industry to ramp up capacity to meet higher demand.