Russia’s strategy for seizing territory in Ukraine’s Donbas region carries implications far beyond the battlefield.

Over the past month, Moscow’s troops have pushed to expand and consolidate areas they hold across easternmost Ukraine, aiming to entrap Ukrainian troops along the way. Russian forces, having scaled back earlier ambitions for a broad thrust, are advancing by unleashing intense artillery fire and air attacks in limited areas, aiming to throw back Ukrainian defenders. Moscow wants to demonstrate that its military might can grab and retain territory.

Kyiv’s forces have fought back, thwarting Russia’s advance and regaining ground in some areas.

The battle is a test for both sides. Russian success could validate for President Vladimir Putin a shift in tactics from the war’s early days, when his armies failed to take Kyiv, and embolden him to continue advancing west, back toward the capital.

Ukrainian success stymieing the Russians, in contrast, could convince some wary Western leaders that Kyiv has a chance of prevailing against bigger Russian forces and eventually give Ukraine a better bargaining position with Moscow.

Swaying skeptical European leaders may be more pressing than jockeying for negotiating position against Russia because no such talks appear imminent, while Ukraine is pushing for urgent deliveries of Western heavy weaponry.

Comments by French President Emmanuel Macron last week that the West shouldn’t humiliate Russia have aggravated a simmering dispute among Western countries. On one side are those seeking to aggressively arm Ukrainian forces, including the U.S., the U.K., Poland, the Baltic states and Nordic countries, which see a historic opportunity to reduce Russia’s ability to threaten them militarily.

An injured fighter of the Ukrainian Foreign legion sits in an armored vehicle near the front line, in the city of Severodonetsk in eastern Ukraine, earlier this month.

Photo: str/Shutterstock

A car burned during the Russian shelling of Slovyansk last month.

Photo: Serhii Korovayny for The Wall Street Journal

The other group is led by France and Germany, where many officials are skeptical of Ukraine’s ability to dislodge better-armed Russian forces and fear growing economic damage from the war. Mr. Macron’s statement in an interview with regional French newspapers that “Russia shouldn’t be humiliated” so diplomacy is possible when fighting stops drew a harsh response from Ukraine’s government and withering criticism from other quarters.

“We all better focus on how to put Russia in its place,” Ukrainian Foreign Minister Dmytro Kuleba

responded to Mr. Macron on Twitter. “This will bring peace and save lives.”

The war of words within anti-Russian forces has intensified since Moscow’s troops have pushed deeper into Ukraine’s east by attacking with vast amounts of artillery, supported by infantry to grab the pounded territory. The approach, widely used for a century through the Korean War, can be brutally effective at gaining terrain but requires supporting resources to ensure that captured ground can be held and defended.

Counterattacks by Ukrainian forces over recent days suggest that even as Russian forces advance west, they will face hurdles protecting their rear and supply lines trailing back east.

Russia’s artillery-led drive into Donbas is a much more traditional approach to fighting than Moscow attempted in late February, and closer to Russian military doctrine, say Western military analysts. By sticking closer to tactics that the Russian army was built to follow, its troops have gained more ground, the analysts say.

“The Russians are counting on the fact that they can mass fires and gain as much ground as possible” before their attacking force is effectively blunted or runs out of steam, said Gordon “Skip” Davis, a retired Army major general and former North Atlantic Treaty Organization deputy assistant secretary-general. Russia’s push is costing Moscow heavily in materiel and lives, Gen. Davis said.

The invasion launched on Feb. 24 began with an attempt at a lightning strike on Ukraine’s capital, Kyiv, and other cities in the north, as well as attacks on the east and south by other Russian forces. Russia’s fast-moving air-and-ground assault lacked sufficient punch and faced stronger resistance than it was ready to handle. Weeks later, the bloodied forces withdrew and Moscow regrouped for a fresh push in Ukraine’s east.

A Ukrainian military truck near the city of Kramatorsk in eastern Ukraine.

Photo: Serhii Korovayny for The Wall Street Journal

Soon after that retreat, Ukrainian politicians and Western military leaders warned that the war’s next phase would resemble battles not seen in Europe in generations. Mr. Kuleba, at NATO headquarters in early April, predicted that the battle for Donbas “will remind you of World War II.”

Since then, Moscow’s forces have pushed west from territory along Ukraine’s eastern border that Russian proxies took in 2014 and Russia recognized as independent just before invading in February. Russians have since slowly taken rail links that they can use for provisioning and advanced in an attempt to encircle Ukrainian troops.

Last week, Russian forces pushed into the city of Severodonetsk, the capital of the Luhansk region, which alongside the Donetsk region makes up Donbas. The battle is drawing Western attention in part because Russian success grabbing the city against Ukrainian counterattacks could allow the Kremlin to claim it achieved a significant portion of its recently stated objective of “liberating” Donbas.

“While the Russians are making only slow incremental gains, they are making slow, incremental gains on territory that will matter,” said a senior NATO official.

A senior Ukrainian official said defense forces are now trying to assess the situation in and around Severodonetsk, particularly the condition of bridges and other infrastructure, and judge how it will impact current and future operations.

If Ukrainian forces can stop Russia’s advance at Severodonetsk, it will indicate that Moscow’s concerted effort to break through Ukrainian defenses is less formidable than feared. While immensely lethal and damaging, it is already proving vulnerable to Ukrainian counterstrikes.

“If the Ukrainians can hold the line here, that will matter,” the NATO official said.

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But halting Russia’s advance, if possible, is still likely easier than dislodging Russian troops from Ukraine. Kyiv lacks the volume of firepower that Moscow has moved into Donbas by rail, and is making up for that in many places with agility and by deploying new weapons systems provided by Western allies.

Those systems, such as U.S. M777 towed howitzers and M109 self-propelled howitzers, supplied to Ukraine by several countries and now being deployed at front lines, are far more precise than Russia’s more traditional artillery, which can only target a general area. They are also more mobile, meaning they can move to resupply and aren’t dependent on dedicated supply lines, which can become soft targets.

The U.S. and U.K. have recently pledged to provide even more powerful mobile multiple-launch rocket systems, and other allies have promised additional weaponry including tanks. But Ukrainian government officials say they need larger quantities and yet-more-powerful weapons to secure their country.

Houses destroyed by a Russian rocket attack earlier this month.

Photo: Serhii Korovayny for The Wall Street Journal

A checkpoint in the Donetsk region.

Photo: Serhii Korovayny for The Wall Street Journal

—Vivian Salama contributed to this article

Write to Daniel Michaels at daniel.michaels@wsj.com