In the south, Ukrainian soldiers are fighting on an unforgiving landscape, table-flat farmland with little cover for troops trying to advance.

Sixty miles away, they are attacking across the plains in a coal mining region dotted with slag heaps, pushing toward a strategic railway junction.

Farther east, they are targeting Russian positions on the hills outside Bakhmut, a city in ruins that fell to Russian forces last month after the longest and bloodiest battle of the war.

In fierce battles along the front line this past week, Ukraine’s counteroffensive is taking shape, presenting a major pivot in the war. With each clash, Ukraine is trying to show that it can attack anywhere, while trying to make Russia defend everywhere.

The multipronged assault, concentrated along the front in the south and the east, is a test run of Ukraine’s new arsenal of Western tanks and armored vehicles as well as tens of thousands of newly mobilized soldiers who trained in Europe for months in preparation for the fighting. Kyiv, which as expected in the early stages is suffering casualties, will need to show significant progress in its counteroffensive to keep the money and weapons flowing from the West.

The flurry of initial attacks, staged under a cloak of secrecy by the Ukrainian Army, are intended to probe for weak points and lure Russia into revealing its defensive strategies too soon, before the bulk of Ukraine’s new force is put into the fight. Out in the expanse of farmland, the two armies are maneuvering and hiding their hundreds of tanks, armored vehicles and howitzers in tiny villages and thickets of trees, lest the other side guess where their forces are concentrated.

Once in full motion, Ukraine’s counteroffensive is expected to be one of the largest military operations in Europe since World War II.

Already, Kyiv has deployed soldiers from the 47th Mechanized Brigade, one of nine units formed in October specifically to recapture occupied land and armed with M16 rifles instead of the Kalashnikovs that most Ukrainian soldiers use. On dusty farm roads, American Humvee vehicles bump along over the potholes, Ukrainian flags flapping from their antennas.

Ukraine’s army has sent forward German Leopard 2 tanks and American Bradley infantry fighting vehicles, upgrading its aging fleet of Soviet-legacy armored vehicles. In all, Ukraine has received hundreds of Western tanks, armored vehicles and machines for breaching minefields.

Its forces have been confronting a formidable line of defenses built by the Russians over months with dense layers of mines, trenches and concrete tank barriers. In the tense fighting, some of the new Western weapons have been left behind or destroyed, their battered carcasses shown abandoned amid dirt-crusted fields cratered by artillery in Russian propaganda videos.

The Ukrainian government has been mostly silent about its opening moves, citing the need to maintain an element of surprise. The Russian government has been triumphal in claims of fending off attacks while offering little evidence.

American officials, who said in recent days that the counteroffensive appeared to be underway, have said it is too early to make broad assessments, although they have generally been bullish on the prospects for Ukraine’s counteroffensive.

Each location has a strategic import for Kyiv.

In recent days, fights have been raging both in the Zaporizhzhia region near the farming town of Orikhiv and to the east in the Donetsk region, near Velyka Novosilka, once a sleepy, rural town crisscrossed by country roads surrounded by coal mines and sunflower fields.

Advancing from either of these two sites in the south, long considered a focal point of any Ukrainian counteroffensive, could allow the Ukrainian forces to drive a wedge into Russian-occupied territory, cutting rail and road links and splitting it into two zones. Such gains would give them a chance to cut Russia’s so-called land bridge linking its territory with the Crimean Peninsula — annexed by Moscow in 2014 — which would imperil supply lines.

Ukrainian officials have also said they are pushing on the outskirts of the eastern city of Bakhmut, now a wasteland of burned and collapsed buildings, and almost entirely depopulated. The fighting has raged in rolling hills to the city’s west near an irrigation and drinking water canal, the Donets-Donbas canal.

Because Russia has cast the capture of the ruins as a prize in the war, it must now defend them or risk an embarrassing setback. By attacking here, Ukraine could force Russia to divert resources from defense of the south.

In this opening phase, Ukrainian forces are essentially probing Russian lines to determine the weakest points. They will then try to pivot and concentrate on the assaults that have the best potential for success.

Any fighting is expected to be bloody and brutally violent, with high casualties on the Ukrainian side in assaults.

The attack in the flat farmland in the Zaporizhzhia region is plowing into a dense line of Russian defenses. On a recent drive through the region, villages appeared largely abandoned. At one spot, the only people out were two young boys stomping in a mud puddle, who then scurried off the road as a military truck rumbled past.

The area is one of the shortest routes to splitting Russian-held territory into two sectors but also one of the most heavily fortified.

Commercial satellite images have shown multiple lines of Russian defenses. Russia has spent months laying minefields, digging bunkers and setting out concrete barriers for tanks.

American officials, speaking on the condition of anonymity, confirmed that Ukrainians had suffered losses in the recent fight as did the Russians, but would not quantify the casualties. At least three German-made Leopard 2 tanks and eight American-made Bradley fighting vehicles were recently abandoned by Ukrainian troops or destroyed, based on videos and photographs posted by pro-war Russian bloggers and verified by The New York Times.

At this stage, it remains unclear where Ukraine will land its main blow, Mykhailo Samus, a deputy director at the Center for Army, Conversion and Disarmament Studies, a military research organization in Kyiv, said in a telephone interview. The attacks now are intended primarily to force Russia to reveal its positions and strategies, he said.

As Ukrainian troops assault, Russian forces move reinforcements and fire artillery in response, exposing their positions and defensive strategies. They switch on electronic jamming systems, revealing how this equipment will be used in the fighting.

The Ukrainian military is using what it learns in these assaults to strike Russian artillery positions, said Mr. Samus, softening up defenses for an actual breakthrough battle that will come later. The larger fight “is still ahead of us and where exactly it will be we still don’t know.”

The main Russian defensive tactic, military analysts have said, is to deploy a thinly manned first line to detect an assault as it is overrun. Behind this line are minefields and then more trenches. Even farther back are reinforcements, which rush forward to counterattack the assaulting troops as they try to cross the minefields.

While the fighting could last for months, both sides are quickly shaping their own narrative of success with vague words and few details.

Sergei K. Shoigu, the Russian defense minister, said that forces of Ukraine’s 47th Mechanized Brigade had tried the breakthrough near Velyka Novosilka. The attack, he said, was repelled.

Other announcements have followed a similar pattern, with unsubstantiated claims of Ukrainian attacks being rebuffed and President Vladimir V. Putin even claiming the counteroffensive so far has failed. The seemingly coordinated Russian messaging on the attacks suggested that the state had prepared for how the counteroffensive would be portrayed, according to the Institute for the Study of War, a U.S.-based analytical group.

The group said that Ukraine was attacking in the three areas but achieving only “differential outcomes” and that seesaw fighting, as assault teams push forward and are beaten back, should be expected.

Ukraine has been even more circumspect, largely staying silent on the fighting. In a rare statement on the offensive, President Volodymyr Zelensky of Ukraine said simply that the Ukrainian military had achieved “step by step” results in fierce battles. And Ukraine has closed media access to the front in Zaporizhzhia region.

Maria Varenikova contributed reporting from Zaporizhzhia, and Eric Schmitt from Washington.