When the eastern city of Avdiivka, a Ukrainian stronghold, fell to Russian forces three weeks ago, Kyiv and its allies feared that Moscow’s troops could build on their momentum and quickly press ahead toward strategic military hubs and population centers.

But after making rapid gains in the subsequent days, Russian assaults have stalled around three contested nearby villages. Military experts cite several factors, including terrain that does not favor offensive operations, Russian troops exhausted by months of fighting and a Ukrainian army that has committed significant forces to defending the area.

Russia seems to be maintaining its initiative on the battlefield, and military analysts say its forces could still break through Ukrainian lines in the near future, especially since Kyiv’s defensive efforts are increasingly curtailed by the absence of further American military aid.

Yet for now, they say the fighting appears to have reverted to the kind of inconclusive back-and-forth battles that have characterized much of the war’s front line combat this past year.

“The capture of Avdiivka has not led to the collapse of Ukrainian lines, the possibility for the Russians to move onto open ground or even to make major gains,” said Thibault Fouillet, the deputy director of the Institute for Strategic and Defense Studies, a French research center. “There’s no decisive action or breakthrough.”

It’s a contrast to the situation that emerged from the fall of Avdiivka in mid-February. At that time, as Ukraine’s forces retreated, Russia advanced rapidly, aided in part by the absence of strong Ukrainian defensive positions. Russian troops captured three settlements and took control of nine square miles of land, according to open-source maps of the battlefield.

But in the past 10 days, Moscow has captured only a little over a square mile of land, according to the open-source maps. Its soldiers have been caught up in fighting in and around the villages of Berdychi, Orlivka and Tonenke.

Russian forces “seem to be attempting to push forward using small infantry assault groups, but are being decimated in the relatively open terrain west of Avdiivka,” said Pasi Paroinen, an analyst with the Black Bird Group, a Finland-based open-source community that assesses satellite imagery and social media content from the battlefield.

The recent fighting has also come at a cost to the Ukrainian army, which appears to have now committed some of its best troops and weapons to the fight in the area west of Avdiivka.

Its 47th Brigade, which the United States trained and equipped last year, has been defending Berdychi. A video released by Ukraine’s defense ministry purported to show the brigade using an American-made Abrams tank, one of the United States’ most advanced.

The Ukrainian army “is allocating all possible weapons” to the fight outside Avdiivka, said Serhii Kuzan, the chairman of the Ukrainian Security and Cooperation Center, a nongovernmental research group.

But three of Ukraine’s Abrams tanks have been destroyed or damaged and abandoned there in the past two weeks, according to Oryx, a military analysis website that counts losses based on visual evidence.

Ukrainian forces also suffered heavy losses as they fought off Russian assaults on Avdiivka for months.

Military experts say that Ukraine’s continued defense in the area is likely intended to give its units time to prepare and reinforce new defensive lines further west. The Ukrainian army recently published photos of fortifications that it said it was building near the Avdiivka battle zone, including 6.5-foot-deep trenches and anti-tank ditches.

“You’ve got a stronghold that’s fallen,” Mr. Fouillet said, referring to Avdiivka, “so you need time to put a defensive line back in place.”

Russia’s assault on Avdiivka resulted in heavy human and material losses for its forces. British military intelligence said that the average daily number of Russian troops killed and wounded in February, when Moscow was devoting a large number of forces to the fight for Avdiivka, had reached 983, “the highest rate since the start of the war.”

Mr. Paroinen and Mr. Kuzan noted that Ukraine’s forces have benefited from the area’s terrain. While Russian troops have been attacking Berdychi, Orlivka and Tonenke through open fields with little cover, Ukrainian units hold the high ground in the villages, making it easier to target approaching Russian soldiers.

Should Russian troops eventually capture the three villages, it is unclear what their exact next steps would be, given that the terrain is hilly and dotted with streams and reservoirs, complicating further advances.

Mr. Kuzan said that Russia’s army was currently attacking multiple places all along the more than 600-mile front line to probe Ukraine’s defenses.

“Which of them will be prioritized, for example, in two days or next week, will depend on how well they succeed in pushing through our defense,” he said. “Where they succeed in pushing through, they will deploy additional reserves to build on their success. This is their strategy.”