American and European officials say it is key for Ukraine to cut off, or at least squeeze, the so-called land bridge: the large swath of territory Russia seized between its border and the peninsula of Crimea, which has become a main supply route for the military stronghold it has built there.

Kyiv wants to reclaim its southeastern coast on the Sea of Azov. If Ukraine can drive its forces to the coastline, cutting off Crimea, Mr. Zelensky could count that as a huge win. But even if Ukrainian forces did not reach the sea, and instead took midsize cities in southern Ukraine, that would effectively narrow the land bridge.

From those positions, Ukrainian forces could use medium-range artillery to threaten Russian command posts on Crimea and any military supply convoys Russia sends along the coastline. While the Russian forces in Crimea are currently well supplied, American officials said, laying siege to the land bridge would make the winter difficult for them.

Retaking land is one thing, but what is crucial, American officials said, is for Ukrainian forces to hold on to it.

Essentially, the United States and its allies will be looking at the counteroffensive for evidence that their plan of remaking the Ukrainian army into a modern force that fights with NATO tactics, and that can use complex maneuvers and advanced equipment to allow a smaller force to defeat a larger one, is sound.