Russia’s advances in eastern Ukraine have been costly.

It has been two months since the Kremlin began its large-scale assault on the eastern Donbas region of Ukraine, directing the force of its vast arsenal along a 300-mile front and inflicting heavy losses on Ukrainian forces as its fighters blasted their way to grueling gains.

Russia now controls 80 to 90 percent of the region, according to estimates. But the campaign has come at a high price. After weeks of bloody battles and persistent defense by outgunned Ukrainian soldiers, Russia’s forces are likely to be severely depleted of both men and equipment.

An entire Russian regiment — which when fully staffed could include several thousand troops — was forced to withdraw from the eastern front “to restore combat capability” after suffering heavy losses, the Ukrainian military said on Saturday. The Ukrainians also said they had destroyed “30 units of various equipment and weapons of the enemy” in the 24 hours starting Friday morning. Russia “continues to suffer significant losses,” the Ukrainians said late Saturday.

The claims could not be independently verified, but if confirmed they would be signs that the battle for control of the Donbas is taking a steep toll on Russian forces already battered in the early months of the war as they tried and failed to seize Kyiv, the capital, and other towns and cities in the north.

“The Russians have lost probably somewhere in the tune of 20 to 30 percent of their armored force,” Gen. Mark A. Milley, the chairman of the U.S. Joint Chiefs of Staff, said last week. “That’s huge. So the Ukrainians are fighting a very effective fight tactically with both fires and maneuver.”

General Milley said that “the numbers clearly favor the Russians” when it comes to weapons, making the additional $1 billion the White House pledged to Ukraine for more artillery, rocket systems, coastal defense weapons and ammunition critical.

As Ukraine anxiously waits for weapons to arrive, Russian forces are killing as many as 200 Ukrainian soldiers every day, Ukrainian officials say. The Ukrainians are desperately trying to hold their ground in the ruined city of Sievierodonetsk, as they also defend against a wider encirclement of their forces in the area by Russians advancing from the north, south and east.

Unable to dislodge the Ukrainians from Sievierodonetsk after weeks of intense bombardment and urban combat, Russia was trying to improve its “tactical situation” by carrying out assault operations outside the city, the Ukrainian military said on Saturday.

“Now the most fierce battles are near Sievierodonetsk,” said Serhiy Haidai, the regional governor for Luhansk Province, which forms part of Donbas.

Michael Kofman, the director of Russia studies at CNA, a research group in Virginia, said in a recent analysis that if the Russians broke through in Sievierodonetsk, their manpower struggles could still impair their ability to sustain any advance.

“The Russian military has spent months trying to hire additional contract servicemen, deploying reservists, and now organizing additional battalions based on existing force structure,” Mr. Kofman wrote, adding: “These are piecemeal efforts that allow the Russian military to sustain itself in the war, but do not address the fundamental deficit in manpower.”

The British military intelligence agency reported on Sunday that the fierce, slow fighting in the east was likely to be taking a toll on the morale of both armies.

“Ukrainian forces have likely suffered desertions in recent weeks,” the agency said in its latest public assessment. But it described the problems in Russian ranks as more systemic and severe, including “cases of whole Russian units refusing orders and armed standoffs between officers and their troops.”

“Morale problems in the Russian force are likely so significant that they are limiting Russia’s ability to achieve operational objectives,” it said.

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