At the first whistle of an incoming shell, the soldiers in a newly liberated but desolate Ukrainian village dived into the weeds on a roadside on Thursday and lay face down as explosions erupted.

“Is everybody alive?” one yelled when it was over. They were. The soldiers sprang back up and kept running, passing the wafting smoke from explosions.

After months of preparation and bolstered by hundreds of Western-donated tanks, armored vehicles and howitzers, Kyiv has notched small successes in the first week and a half of a counteroffensive to drive Russian forces from southern Ukraine. In fierce fighting on the plains, the military said it had broken through a first line of Russian defenses and reclaimed seven villages.

The fruits of their labor could be seen on a visit with the Ukrainian military to one of those villages, Blahodatne, on Thursday — as well as the daunting challenges that lie ahead.

Ukraine has yet to commit the bulk of its reserves, including troops trained in Europe over the winter and spring, and equipped with weaponry from NATO countries, meaning it can bring still more force to bear. But with each step forward, its soldiers become more vulnerable — removed from the safety of their own trenches, closer to Russian artillery, maneuvering through minefields and unprotected from airstrikes.

Ukraine is engaged in two main thrusts southward, where it has broken through most deeply in the string of small villages that includes Blahodatne, where the soldiers were diving for cover on Thursday.

For Ukrainian soldiers with the 68th Scout Brigade who entered the villages, the sweetness of liberating land was tempered by the panorama of ruin that greeted them and what came next: a relentless bombardment from Russian forces.

“They are attacking with rockets, howitzers, mortars, helicopters and drones,” Sgt. Serhiy Gubanov said in an interview while taking cover in a basement as explosions boomed outside.

“It’s the complete collection of intense experiences,” he said.

At one moment, the metallic shriek of an incoming howitzer round sent all the soldiers in the abandoned house, including the basement, to the floor. But there was no explosion. “Dud,” one said, getting up and dusting himself off.

Russia’s main defensive line, about nine miles away from the village, is a dense belt of minefields, trenches, ditches to block armored vehicles and concrete barriers — known as dragons teeth — spread in lines over fields and intended to stop tanks.

After the first week and a half of fighting, Russia’s strategy, too, is coming into focus, Rob Lee, a senior fellow with the Foreign Policy Research Institute, said in a telephone interview.

The Russians are trying to inflict as many casualties and destroy as many vehicles as possible in a battle zone ahead of the main defensive line, depleting Ukrainian forces before they reach it. In effect, it turns the area in front of the main defense line into a kill zone.

The Russian strategy, Mr. Lee said, is “to inflict attrition on Ukrainian units and pull back without taking too many losses themselves.”

This is the area where Ukrainian troops now find themselves.

They are especially vulnerable immediately after seizing new ground, when they are still clearing mines, fighting Russian stragglers, and figuring out where to find cover and firing positions in the newly reclaimed villages and in thickets of trees.

If the Russian strategy proves effective, Ukraine could lose too many of its newly trained troops — which number in the tens of thousands — and too many tanks and infantry fighting vehicles to breach the main line.

Even if they get that far, the forces might be too weakened to stream south and help accomplish a major objective: severing the so-called land bridge that connects Russia to the occupied Crimean Peninsula. This would be done by reaching the Sea of Azov, about 60 miles away.

The combat taking place now is primarily in two locations about 50 miles apart, south of Velyka Novosilka and south of Orikhiv. After early uncertainty, these appear to be more than mere feints or probing attacks by Ukraine. By attacking in two places, Ukraine is forcing Russia to decide where to deploy reinforcements.

Both sides are now in a guessing game.

So far, the battle to the south of Velyka Novosilka, fought in the Donetsk region, where shadows of clouds played across fields of high green grass, wildflowers, small lakes and reedy swamps, has gone better for the Ukrainians than the fighting near Orikhiv, which is in the Zaporizhzhia region.

Hanna Malyar, a deputy minister of defense, said Thursday that the counteroffensive was progressing “gradually but steadily.” Gen. Oleksiy Hromov, a deputy commander of operations in the general staff, said Ukraine had advanced in total 6.5 kilometers, or about four miles.

Soldiers in the 68th Brigade said that a company of Russian soldiers — about 100 men — had been cut off while retreating from the village of Blahodatne. The Ukrainians have been hunting for them, while trying to avoid artillery fire.

Those they have captured so far are poorly trained troops, including former convicts, suggesting that Russia had deployed more fighters it considered more expendable near the front while keeping more capable ones in reserve.

Earlier this week, one Ukrainian fighter, Lt. Serhiy Hozhulovsky, driving an American-provided armored vehicle, was transporting one Russian prisoner of war who was bound hand and foot, his eyes covered with duct tape.

In a cellphone video, the captured Russian can be hearing saying he never fired his weapon and asking to be allowed to remain in Ukraine.

“What will you do?” a Ukrainian soldier asks him.

“I will work, I will build houses,” the Russian replies. “It’s a sin to fight. I cannot fight.”

The Ukrainian soldiers say the captives they have picked up over the past week often claim they did not shoot. In fact, many “fight until the end,” said a private, who asked to be identified only by his first name, Mykola.

On Thursday, when the soldiers tasked with finding stragglers first entered the village after the Ukrainian assault teams swept through, it was an eerie, destroyed place. Nearly every house had been blown up, and chest-high weeds grew in yards. Most residents had fled long ago.

At a command post in an abandoned house on Thursday, a radio crackled with news that a mortar shell had hit an armored vehicle, destroying it but not wounding the crew.

One commander, Capt. Volodymyr Rovensk, sat in a darkened room before computer screens, as explosions rattled the house. The Russians nearby, he said, “are dug in and there are mines everywhere.”

Around the village, the detritus of Russian soldiers’ daily lives lay about: discarded cardboard boxes of military rations and, at one site, a book with pornographic pictures titled “The Machine of Love.”

One Ukrainian soldier, Sergeant Yevhen, tried to carry out of the village a Russian Army-issued spoon as a keepsake — but then dropped it in the weeds while diving for cover from the artillery fire.

“It’s no big deal,” he said. “I wasn’t killed. The spoon wasn’t important.”

Maria Varenikova contributed reporting from Konstantinople, Ukraine.