Ukraine and Russia Battle for a Gateway City in the East

Combat raged around the city of Kreminna in eastern Ukraine on Tuesday, as Ukrainian forces edged closer to reclaiming that small but strategically important city, while the Russians battled to defend some of their hardest-fought gains of the war.

Kreminna is a gateway to two much larger cities nearby, Sievierodonetsk and Lysychansk, important industrial centers in the Donbas region that fell to Russia after a grueling and costly summer campaign. President Vladimir V. Putin of Russia has called conquering and annexing the Donbas the heart of the war effort.

Since enduring a series of humiliating retreats, the Russian military has fortified its lines near Kreminna with a series of defensive barriers, part of its effort to solidify its positions up and down a jagged front that stretches for hundreds of miles. Retaking the city and other towns nearby would expand the Ukrainians’ foothold in the region, and give them control of major roads leading to Sievierodonetsk and Lysychansk.

“The situation there is difficult, acute,” President Volodymyr Zelensky of Ukraine said of Kreminna and other areas in eastern Ukraine, in his nightly address late Monday. “The occupiers are using all the resources available to them — and these are significant resources — to squeeze out at least some advance.”

Serhiy Haidai, the Ukrainian regional governor of Luhansk province, said on Monday that, in response to military pressure, part of the Russian command in Kreminna had withdrawn to the town of Rubizhne, a few miles to the southeast, although it was not possible to verify the claim. “The Russians understand that if they lose Kreminna, their entire line of defense will ‘fall,’” he said in a Telegram post on Tuesday.

Vitaly Kiselyov, a Russian-backed official in occupied Luhansk, said on Russian state television on Monday that the situation around Kreminna and another small city nearby, Svatove, remained “very tense.”

The Ukrainian counterattack in the east comes as the country’s battered economy shows new signs of the war’s toll, leaving it ever more dependent on Western aid. The Ukrainian government has struggled to raise money on bond markets, unable to roll over debt accumulated before Russia invaded in late February, and since then has paid investors about $2.2 billion more than it collected in bond sales, the Central Bank said.

Overall, Ukraine’s economy is projected to shrink about 40 percent this year, as Russia occupies about a fifth of its territory, hammers its cities with cruise missiles, and batters critical industries like steel manufacturing and agriculture.

All of that has left Ukrainian public finance, which has been wobbly at the best of times during three decades of independence, deeply reliant on assistance from the United States, the European Union, European countries that donate individually and other donors.

The International Monetary Fund, which bailed out Ukraine through a long run of post-independence financial crises, has not continued large-scale lending during the war. “If the I.M.F. is worried about debt sustainability and ability to finance, imagine what private investors are thinking,” said Tymofiy Mylovanov, a former economy minister who is a professor at the Kyiv School of Economics.

Russia’s economy has also suffered over the 10 months of war, though it has not collapsed under the pressure of punishing Western sanctions. This week, Russian and Ukrainian leaders again suggested they were open to peace talks, but only on terms that were dismissed by their counterparts.

Ukraine’s foreign minister, Dmytro Kuleba, said that his government wanted a “peace summit,” mediated by the United Nations, but that Russia could not be invited until it faced war crimes prosecution. Mr. Putin said he was willing to negotiate — but days earlier he restated a determination to keep fighting, and he has insisted that lands captured by his forces must remain Russian forever.

On Tuesday, Mr. Putin showed no sign that he expected the war, or acrimonious relations with the West, to soon abate. He met with the president of Belarus, raising concerns that he would use that nation — again — to launch an attack on Ukraine. And he signed a long-expected decree that banned sales of oil to nations that imposed a price cap on Russian oil: the European Union and its members, the United States, Britain, Japan, Canada and Australia.

In the absence of diplomacy, Ukraine and Russia’s militaries have been struggling against each other, and muddy winter weather, to seize more ground and entrench what they hold.

Ukraine’s campaign to recapture Kreminna began in the fall, as its forces finished sweeping through the country’s northeastern Kharkiv region and turned south to focus on Luhansk, which was almost entirely under Russian control.

Since then, the sides have fought a series of battles and artillery duels over highways and villages around Kreminna and Svatove. Russian forces took over both places not long after their full-scale invasion began, and have severed pontoon bridges over a river and built layers of defensive lines to shore up the front.

Ukraine and Russia are also locked in fighting hundreds of miles to the southwest, in the Kherson region, where Ukrainian forces pushed Russian troops out of the capital city but the Kremlin still controls a large swath of territory. A Russian artillery strike damaged a kindergarten, infrastructure and an emergency medical aid station on Tuesday in Kherson, although no casualties were reported, the regional governor, Yaroslav Yanushevych, said on Telegram.

Since he took overall command of Russia’s war effort in October, Gen. Sergei Surovikin has sought to rally Russian forces from their series of defeats this fall. He pulled Russian troops out of the city of Kherson in an organized retreat, and has made efforts to conserve Russia’s artillery supplies and reconstitute units, analysts say.

After losing the city of Kherson and suffering other setbacks in the region, Russia has been regrouping and reinforcing its troops in northern Luhansk for an offensive that would aim to extend its control in the region, according to the Institute for the Study of War, a Washington-based research group.

To that end, the institute said, Russia is prioritizing mobilizing troops to defend Kreminna and Svatove over operations in other parts of eastern Ukraine. The institute cited Ukrainian military reports of increased Russian movements of troops, military equipment and ammunition in the area.

It said, however, that Russian success in the short term appeared unlikely given the difficult terrain and the “very limited” offensive capabilities of Moscow’s forces after months of heavy losses. Though a draft in the fall provided Russia with hundreds of thousands of sorely needed troops, artillery-heavy warfare has depleted its best-trained units and strained its supplies.

Ukraine also faces serious supply problems, analysts say, especially as its Western supporters themselves start to run through their stockpiles.

“Ukrainian artillery use, conservatively, is probably around maybe 90,000 rounds per month,” Michael Kofman, the director of Russian studies at C.N.A., a Virginia research institute, said last week on the “War on the Rocks” podcast. “That’s a lot more than anybody makes in the West right now. So all of this has been coming out of stocks, which is like going through your saving accounts.”

He added that Ukrainian leaders were “willing to say what it takes to get the assistance they need” for beating Russian forces back. “I don’t blame them. Their war effort hinges on external material support, that’s basically it.”