Ukraine rushes troops to reinforce its faltering defense of Sievierodonetsk.

LYSYCHANSK, Ukraine — Russian forces mounted an assault on Sunday against a key Ukrainian defensive position near two strategically important eastern cities, Ukrainian military officials said, bringing them a small step closer to encircling thousands of Ukrainian troops.

Ukrainian forces rushed reinforcements to frontline positions around Toshkivka, a small town southeast of the metropolitan area of Sievierodonetsk and Lysychansk. The Russians “had success” but were eventually held off, a Ukrainian official said, but the fight highlighted Ukraine’s faltering defense of two of the last cities in the Luhansk province of the Donbas region that are not yet under Russian control.

If Moscow’s forces succeed in cutting off Sievierodonetsk and Lysychansk, it could strand thousands of Ukrainian fighters defending the cities, deliver a hard-won military victory to Moscow and move its forces closer to President Vladimir V. Putin’s objective of seizing all of Ukraine’s eastern Donbas region.

Ukrainian battle tanks and several Grad multiple launch rocket systems were seen heading in the direction of Toshkivka and other parts of the front line on Sunday afternoon, smoke billowing from their chassis and treads churning up backcountry roads, likely in an effort to push back Russian forces there.

One crew member, when asked if his tank was headed to the Ukrainian defenses in that area, smiled and nodded.

As Russian troops have moved to surround both cities amid weeks of street fighting and artillery duels, Ukrainian forces have fallen back and now hold only a small portion of Sievierodonetsk. That includes a chemical plant where hundreds of civilians are believed to be sheltering and which has come under withering Russian bombardment in recent days, Serhiy Haidai, the governor of Luhansk, said on Sunday.

Fighting continues elsewhere in the region. To the southwest, Ukrainian military officials said Sunday that their troops had successfully repelled an offensive on the eastern outskirts of Berestove. The Ukrainian military’s general staff added that Russia is planning another assault in Sloviansk, about 50 miles directly west of Sievierodonetsk.

Russia’s Defense Ministry did not immediately comment on Toshkivka, but said earlier on Sunday that its forces had seized Metolkine, a town just east of Sievierodonetsk. The Russian state news agency Tass said that many Ukrainian fighters had surrendered there, although it was not possible to independently verify the claims.

Toshkivka has served as an important part of a defensive wall in what has been referred to as the Sievierodonetsk pocket. Situated in the Donbas region — an area of rolling plains, farm fields and coal mining towns, where Moscow has committed the bulk of its military power in recent months — the pocket is about three-quarters encircled by Russian forces. That has left only a slender gap to the west where Ukrainian troops come and go by using village roads that are often targeted by Russian artillery fire.

And Russian troops have been creeping forward to close the gap.

If Ukrainian forces are unable to reinforce the frontline in Toshkivka, it means Russian forces will have tightened the noose from the southern direction, reducing the area for Ukrainian troops to maneuver within the pocket. It would also allow Russian forces to threaten the few remaining Ukrainian supply routes into Lysychansk and Sievierodonetsk.

The president of Ukraine, Volodymyr Zelensky, said earlier this month that the future of much of eastern Ukraine would be decided in the battle for these two cities.

Ukraine’s decision to hold out in street fighting in Sievierodonetsk was a gamble from the start. Its strategy has been to fight at close range in the city, where Russia cannot bring its vast artillery advantage to bear.

But the soldiers in the city, and those supporting them in the neighboring town of Lysychansk on the western bank of the Siversky Donets River, have been at daily risk of being surrounded.

Russian artillery gun lines have pummeled the roads, bridges and Ukrainian positions with what Ukrainian troops estimate are thousands of shells each day.

However risky, Ukraine’s strategy has successfully tied up Russian forces and inflicted casualties, Andriy Zagorodnyuk, a former Ukrainian minister of defense, said in an interview on Sunday.

“Right now, the main objective is to use the window of opportunity that we have to completely exhaust the Russians in the Donbas,” he said.

Besides, he added, it is better to fight now than to retreat and fight later at another site farther to the west.

“If we would move, they would move,” Mr. Zagorodnyuk said. “We would have to meet them somewhere. It’s not like Putin wanted just Sievierodonetsk. They will keep going until they are stopped.”

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