Russian troops defending a pocket of territory wedged between a river and the border with Ukraine were at risk of becoming encircled, military analysts said Monday, after Ukraine bombed bridges that are the only routes for resupply or retreat.

In their counterattack into Russia, which has been underway now for nearly two weeks, Ukrainian troops quickly broke through thinly manned border defenses, fanned out on highways and captured towns and villages, initially pushing deeper into Russian territory.

The bombing of bridges, in contrast, takes aim at land between the Seym River, the border and an area inside Russia already controlled by Ukraine, with the potential to entrap the Russian forces positioned there. Three bridges span this stretch of river, all now destroyed or damaged, according to statements released by the Ukrainian Air Force and to social media posts by Russian officials and military commentators.

“Minus one more bridge!” the Ukrainian Air Force commander, Lt. Gen. Mykola Oleshchuk, wrote in a post on Telegram on Sunday.

The potential encirclement of its forces in the area adds another challenge to a Russian Army caught off guard by Ukraine’s startling incursion over the border on Aug. 6. The operation has injected a new sense of optimism to Ukrainian forces that had been backpedaling for months elsewhere along the front line.

Analysts and Western officials, though, say it is too soon to know whether Ukraine will emerge with a strategic success. In his nightly video address on Sunday, President Volodymyr Zelensky indicated that a goal of the incursion was to form a “buffer zone” inside Russia along the border with his country, though he offered no specifics about how wide a swath his military would seek to seize.

In the fighting swirling over mostly flat plains in Russia and Ukraine, the tactic of seeking to encircle troops has been central to both country’s armies. Becoming surrounded or pinned against a river is a much-feared outcome for soldiers. The envelopments are called, in Russian military parlance, “kettles.”

Earlier in the long-simmering conflict in eastern Ukraine, these tactics have resonated politically, with Ukraine agreeing to a cease-fire in 2015 after thousands of its soldiers were encircled in the town of Debaltseve. In 2022, Russian troops were encircled during a failed river crossing at the village of Bilohorivka that left hundreds dead.

It is unclear how many Russian soldiers remain in the area between the Seym River and the border with Ukraine. The territory includes the town of Glushkovo, with a population before the incursion of about 5,000. Glushkovo is seen as a likely next objective after Ukrainian troops gained control of the Russian town of Sudzha last week.

Russian social media sites posted photographs of one of the bridges still standing after the strike announced on Sunday but with a hole punched in its deck. On Friday, the asphalt surface of the first bridge struck, near Glushkovo, slumped into the roiling river water, a video released by the Ukrainian Air Force showed.

On Monday, Russian military bloggers and a regional official posted that the final bridge in the area had been destroyed. “At night, the enemy hit the third bridge,” Roman Alekhin, an adviser to the governor of the Kursk region, posted on Telegram. He wrote that Russian forces had built pontoon bridges to provide access.

Neither the destruction of the third bridge nor the building of a substitute could be independently verified. Ukraine has not disclosed what weapons it used to hit the bridges.

Russian troops may be forced to withdraw from the area if they are at risk of being cut from resupply or a means of retreating, said Mykola Bielieskov, a military analyst with a Ukrainian nongovernmental group assisting the army, the Come Back Alive foundation.

“Strikes on the bridges complicate, or even completely prevent, the enemy from maintaining their forces south of the Seym River,” he said.

If Ukraine’s forces advance to the riverbank, they would gain the advantage of putting a natural barrier in front of any Russian counterattack.

The strategy of using rivers as protection has become clear as the offensive proceeds, Vasyl Pavlov, a military historian, said. Ukrainian forces advanced along two rivers, the Seym and the Psei, in each case using a waterway as a natural barrier to prevent counterattacks, he said in an interview.

“We see the Ukrainian attacks are oriented parallel to the geographical features,” he said, with a river always covering one side of the Ukrainian assault groups. “It’s been a very successful plan” he added. “The whole attack is covered by two rivers.”

Ukrainian troops have also pressed farther into Russia but encountered resistance. Battlefield maps based on satellite images and open sources such as videos posted online by combatants on both sides have shown the Ukrainians fighting on the outskirts of the town of Korenovo, about 15 miles from the border.

The ultimate military goals remain shrouded in secrecy. But if the Ukrainians do advance deeper into Russia, they could bring key railroad junctions within artillery range.

The Russian military relies heavily on railroads for logistics. Ivan Kyrychevsky, a military analyst, noted in an interview on Ukraine’s Espresso TV that about 900 miles of railroad track in western Russia converge on two junctions in the Kursk region, one at the town of Lgov, now about 21 miles from the Ukrainian advance.

Both Ukrainian and Russian military commentators in the meantime have noted Ukrainian bombardments of the Russian town of Tetkino, on the southern edge of the pocket of land where Russian troops could become trapped. That would put even more pressure on the Russian forces in the area.

A day after Mr. Zelensky said a major goal of the incursion was a buffer zone with Russia, U.S. Defense Secretary Lloyd J. Austin III spoke on Monday to his Ukrainian counterpart, Rustem Umerov, about the operation’s objectives.

“The secretary did get a better understanding from Minister Umerov of what they’re trying to accomplish there,” Sabrina Singh, the deputy Pentagon press secretary, told reporters without elaborating.

Ms. Singh said that the Americans were still seeking additional details from the Ukrainian military.

Asked if Mr. Austin had voiced concern about Ukrainian forces being stretched too thin along the 600-mile front line, Ms. Singh said, “Of course being stretched on the battlefield is something that the secretary discussed.”

Inside Ukraine, the fighting has continued in Moscow’s favor. Russian forces are advancing toward Pokrovsk, a strategic rail and road hub in the eastern Donbas region. The military commandant of the town, Serhii Dobriak, told Radio Liberty on Monday that residents should plan to evacuate within two weeks. Russian forces are now about six miles to the east of Pokrovsk.