Referenews

Ukrainian officials acknowledged Wagner’s advances in Soledar, a resort town of former salt mines with a prewar population of 10,000 people, but denied that it had fallen. Ukrainian soldiers in the area also dismissed Mr. Prigozhin’s claims of encircling Ukrainian forces as propaganda.

Kremlin spokesman Dmitry Peskov told reporters on Wednesday to wait for official statements on the situation in Soledar.

“Let’s not rush,” Mr. Peskov said. “There is a positive momentum of advancement there, but military success will be achieved when we meet the goals set by the commander-in-chief,” he said, referring to Russian President

Vladimir Putin.

Russian advances in Soledar imperil Ukraine’s ability to defend the nearby city of Bakhmut, which Wagner’s troops have been storming for the past six months. A much bigger city and a gateway to the Ukrainian-controlled half of the Donetsk region claimed by Russia, Bakhmut has become a symbol of Ukrainian resistance in the war—and the conflict’s main battlefield in recent weeks. 

Ukrainian President

Volodymyr Zelensky

visited front-line troops in Bakhmut just before flying to the U.S. last month, presenting a flag signed by these soldiers to the U.S. Congress.

Wagner, which has grown to a force of some 50,000 men after recruiting inmates throughout Russia’s prison system, seeks to portray itself as the only Russian unit capable of offensive operations. Mr. Prigozhin, a confidant of Mr. Putin, said in his message from Soledar that no regular Russian troops were involved in battles there.

The Russian Ministry of Defense disputed that. Russian VDV airborne troops were blocking Soledar from the north and the south, the Russian air force was striking Ukrainian positions in the area and other Russian units were fighting inside the town, it said.

Mr. Prigozhin and another warlord with a de facto private army, Chechen leader

Ramzan Kadyrov,

have repeatedly criticized the leadership of the Russian military as incompetent after Moscow lost large parts of the Kharkiv, Donetsk and Kherson regions to Ukrainian offensives in September, October and November. The last time Russia made gains in the war was the seizure of the cities of Severodonetsk and Lysychansk, an operation where Wagner played a major role, in late June and early July. 

As the power struggle between Mr. Prigozhin and the Russian defense establishment burst into the open, Mr. Putin has so far stood by his defense minister,

Sergei Shoigu,

and defense general staff chief, Gen.

Valery Gerasimov.

On Tuesday, Russia’s Ministry of Defense promoted Col. Gen. Alexander Lapin, whom Messrs. Prigozhin and Kadyrov demanded to be punished for Russian defeats in Kharkiv, to chief of staff of Russian Land Forces.

Wagner has transformed itself over the past 11 months from a relatively small elite force that sent mercenaries to Syria and Africa to a multitiered corps-size formation. Highly skilled veterans still command Wagner units and provide artillery and air support. The storming of Ukrainian positions is usually carried out by convicts, who are executed for desertion or cowardice, but have been promised a pardon and a possibility to return home should they survive six months in Ukraine. Mr. Prigozhin this month released the first batch of a few dozen such survivors, many of them missing limbs.

“The enemy pays no attention to huge losses of its personnel and continues the active assault. The approaches to our positions are simply littered with the bodies of the adversary’s dead soldiers,” said Ukraine’s deputy defense minister,

Hanna Malyar.

Ukraine, however, is also taking high casualties on the Bakhmut-Soledar front, quickly depleting the strength of several brigades sent there as reinforcements in the past month.

In May and June, Ukraine made a similar stand in nearby Severodonetsk and Lysychansk, grinding down Russian forces in heavy street battles before eventually retreating to escape encirclement. That neutralized, for a while, Russia’s offensive abilities.

At the time, however, Russia was mostly waging the war with professional contract troops, and suffered from severe manpower shortages. Mr. Putin’s October mobilization of 300,000 reservists, coupled with Wagner’s prison recruitment drive that started in earnest in August, have changed the arithmetic of attrition to be in Russia’s favor. Mr. Prigozhin has said that his goal in the Bakhmut area isn’t so much to seize the city itself as to destroy Ukraine’s most combat-capable forces.

Western—and some Ukrainian—officials, soldiers and analysts increasingly worry that Kyiv has allowed itself to be sucked into the battle for Bakhmut on Russian terms, losing the forces it needs for a planned spring offensive as it stubbornly clings to a town of limited strategic relevance. Some of them say that it would make sense to retreat to a new defensive line on the heights west of Bakhmut while such a pullback can still be organized in a coordinated fashion, preserving the Ukrainian military’s combat strength.

“It’s not me, it’s King Leonidas who figured out that you should fight the enemy on the terrain that is advantageous to you,” said one Ukrainian commander in Bakhmut, referring to the ruler of Sparta who battled the Persian Empire at Thermopylae. “So far, the exchange rate of trading our lives for theirs favors the Russians. If this goes on like this, we could run out.”

—Georgi Kantchev contributed to this article.

Write to Yaroslav Trofimov at yaroslav.trofimov@wsj.com