BAKHMUT, Ukraine — The steady rattle of machine-gun fire resonated across the outskirts of the eastern Ukrainian city of Bakhmut on Saturday morning. The sound, interspersed with the shriek of rockets and mortar fire, indicated one thing: The Russian troops were getting closer.
Bakhmut, a city with a prewar population of 70,000, is critical to Russia’s objective of taking the rest of the mineral-rich Donbas region. When Russian forces captured the industrial city of Lysychansk in early July and cemented their control of Luhansk, one of two provinces in the Donbas, Bakhmut soon became the focus of Russia’s slow advance.
And even after Russia took a crippling defeat in Ukraine’s northeast last week, when its troops lost dozens of villages and roughly a thousand square miles of territory around the city of Kharkiv, its forces still continued to attack Bakhmut.
Ukrainian soldiers and commanders believe Bakhmut is in an increasingly tenuous position as Russian forces press from the east and southeast in an attempt to cut off the country’s supplies.
Soldiers on the front line around the city have claimed that Russian forces in the area are mainly composed of troops from the Wagner Group, a private military company with ties to the Kremlin. Wagner troops have fought in places such as Syria and Libya — countries with a history of Russian intervention — and Ukrainian soldiers say they are deploying Russian prisoners onto the front lines.
That the Ukrainian forces were being attacked by inmates — and not just regular Russian ranks — suggested a reason there seemed an unending supply of soldiers around Bakhmut attacking them, Ukrainian troops said.
On Tuesday, a video posted online and analyzed by The New York Times shows the Wagner Group promising convicts that they will be released from prison in return for a six-month combat tour in Ukraine. It is unclear when the video was filmed.
After Russia’s humiliating defeat around Ukraine’s capital, Kyiv, in the spring, President Vladimir V. Putin of Russia said that capturing the Donbas, a region roughly the size of New Hampshire, would be one of the war’s primary aims.
At a regional summit in Uzbekistan on Friday, Mr. Putin reiterated that the “main goal” of his “special military operation” was to seize the Donbas, despite losses in the northeast and Ukraine’s ongoing offensive in the south, near the port city of Kherson.
Russian troops currently control much of the Donbas, a region of rolling hills, mining towns and sunflower fields that seem to scrape against the sky. Moscow’s dominance there stems from military advances earlier this summer and the creation of the Donetsk and Luhansk breakaway republics by Russian-backed separatists in 2014.
In the southeastern corner of the Donbas, Russian forces recently made small advances farther west, all but capturing the village of Pisky near the Donetsk airport. But Moscow’s troops have encountered well-manned secondary and tertiary Ukrainian defensive lines that have been in place for years.
As winter approaches, Ukrainian forces are in a position to reclaim some of Russia’s summer gains in the Donbas, especially around the small city of Lyman, an important railway juncture. It has been further isolated from Russian resupply following Ukraine’s recent capture of Izium and Kupyansk in the northwest.
Lyman sits on the northeastern side of the Seversky Donets, a river that has given the Russian forces a de facto defensive boundary for much of the war. If Lyman falls under Ukrainian control, commanders and soldiers said, they will be in a far more advantageous position to repel future Russian offensives.