More than two weeks into Ukraine’s incursion into western Russia, Ukrainian politicians have begun talking about establishing a buffer zone there. But how much farther Ukraine might try to advance into Russia, and how long it plans to stay, is unclear, U.S. officials said.

Ukrainian forces have pushed out in different directions after quickly breaking through thinly manned border defenses early this month. They have broadened their incursion wherever they find the least resistance, setting the contours of what could be a defensible buffer zone to protect Ukrainian towns and villages, which President Volodymyr Zelensky now says is a primary objective of the attack.

After the first week of fighting, Ukraine claimed to control almost 400 square miles of Russian territory — an area roughly the size of Los Angeles.

But American officials are not convinced that Ukraine intends to hold its position in Russia long term. Ukrainian forces have not been digging the kind of extensive trenches necessary to protect soldiers and equipment from enemy fire, if Russia musters enough firepower to repel the attack. They have not been laying minefields to slow down a counterattack, nor have they constructed barriers to slow down Russian tanks, the officials say.

“What the war has shown us so far is that the way to slow a military down is through ‘defense in depth,’” said Seth G. Jones, a senior vice president with the Center for Strategic and International Studies, in a reference to the strategy of using multiple layers of defensive positioning. “If they are not defending territory with a mixture of trenches and mines, it is going to be virtually impossible to hold territory.”

And the more territory Ukraine captures, the greater the challenge it will be for the some 10,000 Ukrainian troops there to defend it, U.S. officials and analysts said.

A Pentagon official said Ukraine’s delay in building defensive fortifications did not necessarily mean that Kyiv did not intend to hold territory in Russia. Ukraine could look to build defensive positions even deeper inside Russia, extending the territory it has seized in order to add to Mr. Zelensky’s buffer zone, the official said, speaking on the condition of anonymity to discuss operational planning.

While the Ukrainians’ initial attack was carefully planned, it succeeded far beyond their original goals, and they now have a more ad hoc strategy that has taken advantage of Russia’s slow and disjointed response, officials said.

Frederick B. Hodges, a retired lieutenant general and former top U.S. Army commander in Europe, said some of Ukraine’s success had resulted from Russia’s “confused and ineffective” military command and control structure. For one thing, he said, two different national security entities run Russia’s military operations.

In eastern Ukraine, where Russia has been making slow gains, the Russian military’s general staff is in charge. But the F.S.B. — Russia’s security agency and the successor to the K.G.B. — is responsible for the response to the Ukrainian incursion.

General Hodges said the rivalries within the Russian security ranks were made clear last year after the short-lived mutiny against President Vladimir V. Putin. “I don’t imagine that the general staff is in a hurry to divert forces to help F.S.B. leadership,” he said.

Russia’s logistics and supply issues have also aided Ukraine.

Russia most likely needs 15 to 20 brigades — at least 50,000 troops — to push Ukraine out of Kursk, officials said, and has nowhere near that number of forces there now. The Russian defense minister, Andrei R. Belousov, said this week that a new coordinating body was “already” working around the clock to figure out how new groupings of Russian troops might counterattack in Kursk.

“It’s had a shocking effect on the Russians,” Gen. Christopher G. Cavoli, NATO’s top military commander, said last week at the Council on Foreign Relations. “They’re shocked by it. That won’t persist forever. They’ll gather themselves together and react accordingly.”

Ukraine’s offensive so far has captured several settlements and one town in Russia, but it has yet to fulfill a key goal: drawing significant numbers of Russian units from eastern Ukraine.

Russia has sent mostly reserve units and troops from areas in southern and northeastern Ukraine that are not part of Moscow’s main thrust toward the city of Pokrovsk.

The U.S. defense secretary, Lloyd J. Austin III, spoke to his Ukrainian counterpart, Rustem Umerov, on Monday about the offensive’s objectives. American officials insist they received no warning from Ukraine that it was going to launch a surprise attack.

“When it comes to Kursk, we have an understanding, from what President Zelensky laid out, that they want to create a buffer zone,” Sabrina Singh, the deputy Pentagon press secretary, told reporters on Thursday. “We are still working with Ukraine on how that fits into their strategic objectives on the battlefield itself.”

“Is their intention to continue to hold?” Ms. Singh said, adding: “How large are they going to expand? These are some of the questions that we’re asking.”

Asked earlier in the week 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.”

Some American officials say that the more land Ukraine tries to take in western Russia, the greater the risk of overextending its supply lines and air defense umbrella. And pushing more forces into Kursk creates weaknesses along the front lines in eastern Ukraine, especially in the Donbas region, where its forces are facing an intense Russian assault.

“Ukraine has expanded the front line, which carries a certain risk in that it requires more personnel and equipment to hold that line — which in turn might deplete some other part of the front or, more likely, reduce their available reserves,” said James Rands, an analyst with the British security intelligence firm Janes.

Ironically, American military officials say that with the Kursk offensive, Ukraine has finally managed to show that it knows how to conduct “combined arms” maneuvering — synchronized attacks by infantry, armor and artillery forces. During Ukraine’s failed counteroffensive a year ago, its forces struggled with combined arms, despite months of training.

“The administration appreciates the risk the Ukrainians took, and are sufficiently impressed at the command and control and coordination that they displayed,” said Evelyn Farkas, the former top Pentagon official for Ukraine in the Obama administration.