Fierce Battle Rages for ‘Every Stairwell’ in Bakhmut, Russian Paramilitary Leader Says

A fierce fight was raging on Sunday in the eastern Ukrainian city of Bakhmut, where a Russian paramilitary leader said Ukrainian forces were defending “every street, every house, every stairwell,” as they waged a desperate effort to deny Moscow its first significant battlefield success in months.

Yevgeny Prigozhin, the founder of the Wagner private military company, whose forces have helped lead Russia’s brutal campaign in Bakhmut, denied reports on social media that Ukrainian forces were retreating from the city.

“The Armed Forces of Ukraine are not retreating anywhere,” Mr. Prigozhin said in a statement posted by one of his companies on Telegram, the social messaging app. “The Armed Forces of Ukraine are fighting to the last.”

Russian forces since last summer have bombarded Bakhmut, a city once home to 70,000 people in the eastern Donbas region of Ukraine, which President Vladimir V. Putin has ordered his forces to capture completely.

In recent weeks, pouring more troops into Donbas and intensifying artillery strikes, Russia has steadily surrounded Bakhmut from three sides and cut off many of the roads leading into and out of the city. That has left Ukrainian forces with one westbound road as their last major supply line — or potential escape route.

“Bakhmut is increasingly isolated,” Britain’s defense intelligence agency reported on Sunday.

President Volodymyr Zelensky of Ukraine on Saturday night called the situation in Bakhmut and other parts of the east “very difficult,” saying that Russia was throwing “more and more of its forces to break our defenses.”

Ukraine also has deployed a large military presence in the region around Bakhmut, with large troop transports and armored vehicles crowding the roads. But some Ukrainian soldiers deployed there have become increasingly pessimistic about the fate of the city amid continuing Russian assaults. They are killing Russians, one soldier recently told The New York Times, but not fast enough.

On Sunday morning, Russian forces struck a school that Ukrainian soldiers appeared to be using as a base in the town of Druzhkivka, west of Bakhmut. The blast ripped out window frames and damaged the facade of the school. Another missile hit an apartment complex directly across from the school, blasting a large hole through the first floor and cutting through a number of apartments. It was not immediately clear if anyone was hurt.

Three people were killed in Russian attacks on Saturday in Bakhmut, the head of the regional military administration, Pavlo Kyrylenko, said on Telegram. A fourth was killed in the settlement of Yampol, to the north, he said.

Still, Ukraine’s defense has drawn in a significant Russian force, pinning them down and preventing them from deploying to other fronts amid warnings that Moscow is preparing to unleash a broader offensive. Mr. Zelensky declared on Friday that the city was “our fortress” and vowed, “No one will give away Bakhmut.”

Michael Schwirtz and Thomas Gibbons-Neff contributed reporting.