After some of the war’s hardest and bloodiest combat, the commander of Russia’s Wagner mercenary organization announced on Tuesday that his soldiers held more than 80% of the damaged eastern Ukrainian city of Bakhmut.

Top Ukrainian military authorities did not explicitly address the charges, but claimed their soldiers were standing fast despite ferocious strikes in what was once a 70,000-person city and keeping Russian forces at bay.

Wagner fighters have led Russia’s months-long efforts to capture Bakhmut. The grinding trench warfare and constant artillery barrages have drawn comparisons with World War One because of massive casualties inflicted on both sides.

Wagner head Yevgeny Prigozhin said his forces, who have played a major role in Russian advances in the east, were pressing on with their encirclement of Bakhmut.

“In Bakhmut, the larger part, more than 80% is now under our control, including the whole administrative centre, factories, warehouses, the administration of the city,” he said in a video posted by a Russian military blogger.

The Russian-installed head of Donetsk region, one of four areas declared annexed by Moscow last September, said Russian forces had backed Ukrainian defenders into a corner.

“In the western areas where their units are dug in, they have no choice other than coming forward and giving themselves up,” Russian news agencies quoted Denis Pushilin as telling state television.

Serhiy Cherevatyi, a spokesman for Ukraine’s Eastern Military Command, said the situation in Bakhmut was under control, adding Kyiv would not allow its troops to be encircled.

Deputy Ukrainian Defence Minister Hanna Malyar acknowledged that Bakhmut “took the main hit” in fighting. But Russian forces, she said, “are generally losing to us in street battles so they are simply destroying all buildings and structures”.

Kyiv says it needs more and better Western weapons to beat Russia, and senior Ukrainian officials pressed ahead with their bid to persuade allies to open up stockpiles.