KYIV, Ukraine (AP) — The fate of a devastated salt-mining town in eastern Ukraine hung in the balance Wednesday as Ukraine said its forces were holding out against a furious Russian onslaught in one of the fiercest and costliest recent ground battles of the nearly 11-month war.

Soledar was under heavy shelling by Russian forces using jets, mortars and rockets. A Ukrainian military officer near Soledar said the Russian assault was unrelenting.

The Russians first send one or two waves of soldiers, many from the private Russian military contractor Wagner Group, who take heavy casualties as they probe the Ukrainian defenses, the officer told The Associated Press.

After those first assaults, when Ukrainian troops have taken some casualties and are exhausted, the Russians send a fresh wave of highly-trained soldiers, paratroopers or special forces, said the Ukrainian officer, who insisted on anonymity for security reasons.

Soledar's fall, while unlikely to provide a turning point in the war, would be a prize for a Kremlin starved of good news from the battlefield in recent months.

It would also offer Russian troops a strategic springboard for their efforts to conquer other areas of Donetsk province that remain under Ukrainian control, such as the nearby strategic city of Bakhmut.

Donetsk and neighboring Luhansk province, which together make up the Donbas region bordering Russia, were Moscow's main stated targets in invading Ukraine, but the fighting has stood mostly at a stalemate.

Ukrainian Deputy Defense Minister Hanna Malyar denied Russian claims that Soledar had fallen, but she acknowledged heavy fighting was ongoing.

The spokesman for Ukraine's Eastern Group of Forces, Serhiy Cherevaty, also dismissed the Russian claims.

Late Tuesday, Yevgeny Prigozhin, the owner of the Wagner Group, claimed in audio reports posted on his Russian social media platform that his soldiers had seized control of Soledar, though he also said that fighting continued in a "cauldron" in the city's center.

The AP was unable to verify that claim.

Russian forces had "positive dynamics in advancing" in Soledar, Kremlin spokesman Dmitry Peskov said, but he stopped short of declaring its capture when asked about the claims that it has come under Russian control.

"Let's not rush, and wait for official statements," he said.

Ukrainian President Volodymyr Zelenskyy said this week that "everything is completely destroyed" in the area because of relentless shelling and weeks of close, house-to-house combat.

"The whole land near Soledar is covered with the corpses of the occupiers and scars from the strikes," Zelenskyy said. "This is what madness looks like."

Soledar, known for salt mining and processing, has little intrinsic value. But it lies at a strategic point 10 kilometers (six miles) north of the city of Bakhmut, which Russian forces are aiming to surround.

Taking Bakhmut would disrupt Ukraine's supply lines and open a route for Russian President Vladimir Putin's forces to press toward Kramatorsk and Sloviansk, key Ukrainian strongholds in Donetsk province.

Soledar's fall would make "holding Bakhmut much more precarious for Ukraine," Michael Kofman, the director of Russia Studies at the CAN nonprofit research organization in Arlington, Virginia, noted Wednesday.

The costly war of attrition, with expected heavy casualties, may make Russia's victory as costly as a defeat, however.

"I don't think the outcome at Bakhmut is that significant compared to what it costs Russia to achieve it," Kofman said in a tweet.

The Wagner Group, which now reportedly includes a large contingent of convicts recruited in Russian prisons, has spearheaded the attack on Soledar and Bakhmut.

Western intelligence has estimated that the Wagner Group constitutes up to a quarter of all Russian combatants in Ukraine.

A success in Soledar and Bakhmut would help Prigozhin, who has openly criticized Russia's military leadership, increase his clout at the Kremlin.

Russia illegally annexed Donetsk, Luhansk and two other Ukrainian provinces in September, but its troops have struggled to advance. After Ukrainian forces recaptured the southern city of Kherson in November, the battle heated up around Bakhmut.

The Institute for the Study of War said Russian forces were up against "concerted Ukrainian resistance" around Bakhmut.

"The reality of block-by-block control of terrain in Soledar is obfuscated by the dynamic nature of urban combat ... and Russian forces have largely struggled to make significant tactical gains in the Soledar area for months," the Washington-based think tank said.

An exceptional feature of the fighting near Bakhmut is that some of it has taken place around entrances to disused salt mine tunnels which run for some 200 kilometers (120 miles), according to Western intelligence reports.

Several front-line cities in Donetsk and Luhansk provinces have witnessed intense fighting in recent months. Putin identified the Donbas region as a focus from the war's outset, and where Moscow-backed separatists have fought there since 2014.

Russia captured almost all of Luhansk during the summer. Donetsk escaped the same fate, and the Russian military subsequently poured manpower and resources around Bakhmut.

On a different front, Zelenskyy on Wednesday visited the western city of Lviv and held a high-level meeting on the security situation near Ukraine's border with Kremlin ally Belarus, the president's office said in a statement.

Russia has stationed more than 10,000 of its soldiers in Belarus and conducts regular military drills in the country, which has a roughly 1,000-kilometer (600-mile) border with Ukraine. The Kremlin used Belarus as a staging ground to send troops and missiles into Ukraine when Russia invaded on Feb. 24.

Concerns have risen in recent months about Moscow potentially pressuring Belarus into opening up a new front in Ukraine's west, possibly to target supply routes for Western weapons and other overseas aid that have helped Kyiv's forces sustain a defense and to launch a counteroffensive.

Zelenskyy said there were no immediate worries about Minsk joining the war, but added: "We must be ready," according to the statement.

Meanwhile, Putin claimed Wednesday that Russia had successfully resisted Western pressure, especially sanctions, over its invasion of Ukraine and vowed that the country has enough resources to beef up its military while continuing social programs and meeting other development targets.

"Nothing of what our enemies forecast has happened," Putin said in a video call with top members of his Cabinet.

"We will strengthen our defense capability and will undoubtedly solve all issues related to supplies to military units involved in the special military operation," he said, using the Kremlin's euphemism for the war.

He said Russia has received 200 billion rubles (about $3 billion) in additional revenue from higher oil and gas prices caused by the war.

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