Russia’s expanding military deployments in and around eastern Ukraine in recent days are setting the stage for a new phase of Moscow’s offensive—one that is likely to be very different from the kind of fighting that has characterized the past two months.

This time, the two countries’ militaries will be operating on open terrain well-suited for massed forces and armored thrusts. Russian forces will also be fighting in closer proximity to their bases in western Russia, giving them shorter supply lines, and on territory their commanders know better.

In the initial weeks of the war, Ukraine managed to thwart a Russian push toward Kyiv and in other parts of the country’s north by using small units armed with antitank weapons to ambush unprepared Russian columns. The battles to come are likely to be more conventional fights.

Ukrainian President Volodymyr Zelensky said this past week that Russian forces “are changing their strategy. They are strengthening their forces to push even harder” in the east.

“You could almost say it’s a whole new war now,” said retired Lt. Gen. Ben Hodges, a former commander of the U.S. Army in Europe, who predicts “a classic steel-on-steel, heavy firepower offensive” fight.

Western officials and military experts say that a major Russian goal is to try to cut off some of Ukraine’s best forces, which are positioned opposite the Russian-occupied areas of the Donbas region in southeastern Ukraine.

To do so, Russian forces have been moving south from the area near Kharkiv and are also expected to push north from Mariupol, if they complete their seizure of that port city on the Sea of Azov.

Ukrainian forces have been working to thwart the Russian advance from the north, repeatedly hitting Russian forces around Izyum, and are desperately trying to hold on to Mariupol, even as their supplies of ammunition and food dwindle.

Ukrainians fired a howitzer in late March in the Zaporizhzhia region of the country.

Photo: STRINGER/REUTERS

If Russia gains control of Ukraine’s east, it could then try to push west again. Taking Odessa, the last Black Sea port the Ukrainian government still controls, would turn Ukraine into a landlocked nation. Russian forces could also try to take Dnipro, the southeastern city on the Dnieper River, and attempt a renewed assault on Kyiv.

Both sides are preparing for tougher combat ahead. To bolster Ukraine’s forces, the U.S. has expanded intelligence sharing with Kyiv to include targets in Russian-occupied Donbas and Crimea. For the first time, the U.S. is also sending 155 mm howitzers as part of a fresh infusion of weapons.

Ukrainian forces, however, are confronting a Russian military that has more long-range artillery and armored punch, despite the losses Moscow has suffered during the war. The Ukrainians are also operating at the end of supply lines that stretch back to the country’s western border, where weapons are arriving via Poland, Romania and other neighboring allies.

Kyiv is seeking supplies of heavy weaponry from former Soviet-bloc countries now in the North Atlantic Treaty Organization, including Soviet-era T-72 tanks, multiple-launch rocket systems, long-range air-defense systems and combat aircraft, to better counter the coming Russian offensive.

The U.S. has said it would supply 200 decades-old M-113 armored personnel carriers in addition to the howitzers.

“The terrain is much more wide open, which favors a heavy armor and mobile force as opposed to a skirmish or ambush style force,” said Philip Breedlove, a retired Air Force general who was the top NATO commander when Russia first took Crimea and secured much of Donbas in 2014. “The M-113s are a good capability, but they are not going to stand up against modern weapons.”

Russia, to build up its combat power and fill out units degraded in the earlier fighting, is attempting to mobilize as many as 60,000 reservists. It has also been moving artillery, command-and-control units and helicopters in and around Donbas, which could support operations by the 65 Russian battalion tactical groups the Pentagon says are already fighting in Ukraine. Battalion tactical groups generally have from 700 to 1,000 troops each.

In preparation for a major attack, Russia has conducted airstrikes against Ukrainian weapon depots and logistics to try to hamper the Ukrainians’ ability to resupply its combat forces—what U.S. officials call “shaping operations.” Moscow has also appointed a new commander, Army Gen. Aleksandr Dvornikov.

In the war’s opening stage, poor logistics and coordination among Russia’s ground and air forces contributed to Russia’s failure to achieve its goals, say military analysts. Russia’s supply lines in Donbas are more developed than those it had around Kyiv, said Mason Clark, an analyst at the Institute for the Study of War, a Washington think tank.

Ukraine said it detonated explosives under a bridge in the Kharkiv region last week as a Russian convoy crossed.

Photo: Ukraine Defense Ministry/Associated Press

Russian forces moving toward Mariupol, Ukraine, on Friday.

Photo: STRINGER/REUTERS

“Russia seems to have set out to improve its command-and-control,” said Ben Barry, a former commander of a British armored infantry battalion now at the International Institute for Strategic Studies think tank in London. “A known unknown is whether Russia has sorted its logistics out,” he said.

And while many factors favor the Russians on paper, they struggled to capitalize on superior weaponry and larger numbers during the war’s early weeks. Sweeping maneuvers over flat terrain will require a degree of coordination that the Russian military hasn’t consistently demonstrated. But it will also provide the Russians with an opportunity to try to envelop Ukrainian units and to mass forces to attempt to punch through Ukrainian lines.

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To try to impede Russia’s buildup, Ukrainian special operations forces recently carried out a daring raid in which they planted explosives under a bridge in the Kharkiv region and detonated the charges as a Russian convoy crossed. Details of the operation were posted Thursday by the Ukrainian Defense Ministry on its website, including how other Ukrainian forces then attacked the convoy.

The greater challenge for the Ukrainian forces will be replenishing their units if the conflict turns into a grinding war of attrition. Already, Ukrainian officials have said the country is using ammunition and supplies faster than it has been receiving them. Some important systems that Ukrainians have sought, such as substantial numbers of Eastern European-supplied T-72 tanks and Western antiship missiles to supplement Ukraine’s modest inventory of Neptune missiles, have yet to appear on the battlefield.

“Given their advantages in combat power, I would expect the Russian forces to make some advances. The red blobs on the map are going to move,” said Liam Collins, a retired U.S. Army colonel who helped mentor Ukraine’s forces from 2016 to 2018. “So it will be absolutely critical to keep flowing weapons to the Ukrainians to replace their losses. The Ukrainian force is much smaller. So even if the Russians take more casualties, the constant attrition can work to their advantage.”

Pentagon officials say the intensity of the combat could well exceed the battles that have already transpired in the more than 50-day-old war.

“This will be a knife fight,” said a senior U.S. defense official on Thursday. “This could be very ugly and very bloody.”

Smoke rises over a town in Ukraine’s Donbas region earlier this month.

Photo: fadel senna/Agence France-Presse/Getty Images

—Gordon Lubold contributed to this article.

Write to Michael R. Gordon at michael.gordon@wsj.com and Daniel Michaels at daniel.michaels@wsj.com