Russian Attacks Along a Wide Arc of Ukraine Yield Little but Casualties

KYIV, Ukraine — From Kupiansk in the north to Avdiivka in the south, through Bakhmut, Lyman and dozens of towns in between, Russian forces are attacking along a 160-mile arc in eastern Ukraine in an intensifying struggle for tactical advantage before possible spring offensives.

Heavy fighting was reported on Monday in and around Avdiivka, a town on the front lines for much of the year-old war, which in recent days has once again become a focal point of combat. Russian shells struck an abandoned school in Avdiivka on Monday, killing a woman, according to Andriy Yermak, head of Ukraine’s presidential office, and the Ukrainian military said it had repelled infantry attacks on the town and at least five nearby villages.

In Bakhmut, where the Wagner private military company has seized control of the eastern side of the city, brutal combat is taking place in the streets, the blasted remains of buildings and deep underground in the warrens of mines, according to Russian military bloggers.

“Wagner’s assault units are advancing from several directions, trying to break through the defenses of our troops and advance to the central districts of the city,” Col. Gen. Oleksandr Syrsky, commander of Ukrainian ground forces, said in a statement released by the military. “In the course of fierce battles, our defenders inflict significant losses on the enemy.”

In Kupiansk and surrounding villages, Russia has stepped up shelling and probing ground assaults, and Ukraine has ordered civilians to leave. Russian shelling intensified in Lyman and other towns, as well. According to the Ukrainian military, Russian forces make more than 100 attempts each day to break through their lines.

With few people or intact buildings, the most hotly contested places have little left to offer beyond control of roads and railways that the Kremlin sees as important to its goal of seizing the entire eastern region known as the Donbas. The assaults may also yield better positioning for the next attack, intelligence about the other side’s positions and propaganda value.

But even by those measures, Russian gains are minimal, and they come at a frightful cost on both sides. Western officials and analysts have estimated some 200,000 dead or injured on the Russian side. They do not publicly put numbers to Ukrainian losses but suspect that they are also enormous.

Away from the war zone, Russia said it would not object to extending by 60 days an agreement that allows Ukraine to ship grain to world markets, despite a Russian blockade of Ukraine’s Black Sea ports. But a longer extension, it said, would require easing restrictions on Russia’s own agricultural exports.

Sergei Vershinin, a deputy foreign minister, revealed Russia’s stance on Monday at talks in Geneva on extending the deal, which is set to expire on Saturday. The pact, brokered in July by the United Nations and Turkey, has been vital to lessening worldwide food shortages and price spikes initially caused by the war.

In The Hague, the International Criminal Court plans to open two war-crime cases and seek arrest warrants for several people — how high-ranking is unclear — according to people with knowledge of the decision. The cases charge that Russia has deliberately targeted civilian infrastructure and abducted Ukrainian children and sent them to indoctrination camps.

However important the cases are as a statement of rebuke, no trial is likely to result. Russia will almost certainly refuse to hand over suspects, and the court does not try people in absentia.

On the battlefields in eastern Ukraine, pro-war Russian blogs that have big followings at home take a dim view of how things are going.

Since the start of the war, the Russians have repeatedly tried and failed to seize Avdiivka, though it lies just outside the Russian-held regional capital, Donetsk, and local Russian commanders have reported capturing some nearby villages in recent days.

Vitaliy Barabash, head of Avdiivka’s military administration, said on Ukrainian television over the weekend that Russia “has been massively hitting the villages near and on the way to the town over the past week.” He added, “These villages are being erased.”

But the town itself is strongly fortified by the Ukrainians, and the prospect of Russia’s encircling it “is not even close,” the blogger Igor Strelkov, also known as Igor Girkin, wrote on Monday.

Russian advancement in Bakhmut “is insignificant,” and Ukrainians have waged a “generally successful” campaign there to wear down the attackers and buy time, Mr. Strelkov said. The Ukrainians have a firm hold on the western part of the city, and even if they were to withdraw, he said, it would make little difference to the exhausted Russian forces.

Western military analysts had predicted that Russia, after drafting 300,000 men last fall and pouring many of them into Ukraine, would mount a major new offensive in the spring. Now they wonder whether the Russian military is so depleted that it can manage little more than the kind of attacks already underway.

But the Ukrainians, anticipating a big influx of Western weaponry and fresh troops in the coming weeks and months, are widely expected to mount a counteroffensive. Analysts, Ukrainian officials and even Russian commenters have suggested that it would come on the southwestern part of the front, with the Ukrainians attempting a push east from Kherson and south from Zaporizhzhia toward the city of Melitopol, hoping to sever the land bridge the Russians have seized that links the Crimean peninsula to the eastern Donbas region.

The Russian blog Rybar said on Monday that Ukrainians holding the west bank of the Dnipro River had been using speedboats and drones to reconnoiter Russian positions on the east bank and had delivered boats, barges and units specializing in building pontoon bridges to the Kherson area, signaling preparation for an attack.

In the long-running attempt to conquer Bakhmut, Wagner fighters have led the Russian forces. But Wagner’s efforts have been hindered by political infighting between its self-promoting leader, Yevgeny V. Prigozhin, who is close to President Vladimir V. Putin, and the leadership of the Russian military, whom Mr. Prigozhin criticizes harshly and publicly.

Last year, Mr. Prigozhin swelled his forces by recruiting prisoners, offering them freedom after a tour at the front, but thousands of them have been killed, wounded or captured, and early this year, the Russian government cut off Wagner’s access to more prisoners. More recently, Mr. Prigozhin has complained bitterly that the Russian military was denying his fighters badly needed ammunition.

The Institute for the Study of War, a research group based in Washington, said on Sunday, “The Russian military leadership may be trying to expend Wagner forces — and Prigozhin’s influence — in Bakhmut.”

But Wagner appears to be stepping up its efforts to sign up fighters outside of prisons. The exiled mayor of Melitopol, a Russian-occupied city in the south, said on Monday that Wagner was trying to recruit people there.

And Britain’s Defense Ministry said in an intelligence update that this month, Wagner set up recruiting efforts at dozens of sports centers across Russia and sent “masked Wagner recruiters” to high schools to spur interest in signing up, “distributing questionnaires entitled, ‘Application of a Young Warrior.’”

Marc Santora reported from Kyiv, Ukraine, Matthew Mpoke Bigg from London and Richard Pérez-Peña from Los Angeles. Reporting was contributed by Marlise Simons from Paris and Nick Cumming-Bruce from Geneva.