Russian forces have begun an assault on the town of Sudzha, the main population center in the Kursk region that was captured by Ukraine last year, a top Russian commander said on Tuesday. The advance puts Moscow on the verge of ending the first invasion of Russian territory since World War II.

“We have surrounded Sudzha from almost all sides,” Lt. Gen. Apti Alaudinov, a top Russian commander in Kursk, told Russian state television on Tuesday.

Russia’s recent rapid moves around Sudzha have erased a large share of the territorial gains made by Ukrainian forces during their surprise attack into western Russia in August. Kyiv had held on to territory in Kursk despite heavy casualties in the hope of using it as a bargaining chip in peace talks.

Amid Ukraine’s advance, 2,000 to 3,000 Russian civilians had taken refuge in Sudzha by February, according to Russian activists and Ukrainian officials. Their fate is unclear.

By Tuesday afternoon, Ukrainian forces had retreated from the eastern side of town across the Psel River, Ian Matveev, an antiwar Russian military analyst, wrote on his Telegram channel. He cited videos posted on social media of Russian soldiers in the town. Deepstate, a Ukrainian group with ties to the Ukrainian Army that maps the battlefield, made a similar assessment on Tuesday.

Mr. Matveev wrote that it remained unclear whether Ukrainian soldiers would try to mount a defense in the western side of Sudzha or continue retreating toward the Ukrainian border, a few miles west.

On Tuesday morning, Russian state media published a photo of a Russian soldier standing at the eastern entrance of Sudzha, a county seat in Kursk that became the main logistical and administrative hub for Ukraine’s occupation forces. The New York Times verified the location of the photo.

On Tuesday morning, the Russian Defense Ministry claimed that its forces had liberated 12 Kursk villages and 38 square miles in the past 24 hours, and analysts speculated that Ukraine’s presence in Russia could end within days.

The Kursk offensive is part of a wider effort by Russia and Ukraine to improve their positions ahead of peace talks mediated by the Trump administration, the Russian military analyst Valery Shiryaev wrote on his Telegram channel on Monday.

As Moscow’s forces pressed forward in Kursk, Ukraine on Tuesday launched the largest drone attack on Russian cities since the start of the war, a move that analysts interpreted as an attempt by Kyiv to show Washington that it can still take the fight to the enemy.

“Everyone is putting on the table the cards that they have,” Mr. Shiryaev wrote.

The rapid crumbling of Ukrainian defenses around Sudzha signals an end to Kyiv’s determined attempts to hold on to captured Russian territory, which at its peak measured more than 500 square miles. To keep the territory, Ukraine had transferred to Kursk some of its best reserves, a strategy that critics said weakened Kyiv’s ability to defend itself against Russian attacks in eastern Ukraine.

Ukrainian officials have repeatedly defended their strategy in Kursk in political terms, saying that territory could be traded for land that Russia has occupied in Ukraine — a possibility that was vanishing rapidly by Tuesday.

Russian soldiers and commanders fighting in Kursk previously said in interviews that they had expected the battle for Sudzha to last months and become one of the bloodiest standoffs of the three-year war, which began with Russia’s full-scale invasion of Ukraine in 2022. It had taken Moscow’s soldiers half a year to grind through Ukrainian defenses and reach the outskirts of the town earlier this year — at the cost of thousands of casualties by most estimates.

Ukraine’s glacial retreat suddenly turned into a rout in the past week.

Russian military analysts said the breakthrough in Kursk begun on Saturday with a surprise attack on the Ukrainian rear. Russian officials said 800 fighters walked about 10 miles through a disused gas pipeline measuring 4.5 feet wide to emerge inside Ukrainian-held territory and engage the enemy in Sudzha’s northern suburbs.

Russian propagandists and officials described the operation as a heroic feat, while Ukrainian sources called it a death sentence, with some Russian attackers allegedly suffocating from residual methane in the pipeline. That claim could not be independently verified.

“I respect them for this creativity,” said a Ukrainian military official who spoke on the condition of anonymity because he was not authorized to speak publicly. He added that the Russian attackers had suffered heavy casualties and that only 90 had made it from the pipeline into Sudzha.

While the effectiveness of the pipeline operation is debatable, it coincided with breaches of Ukrainian defenses by Russian troops in several parts of Kursk.

Ukraine’s top military commander, Gen. Oleksandr Syrsky, said on Monday night that Kyiv was dispatching reinforcements to Kursk, but rejected Russian claims that a large contingent of Ukrainian soldiers there was at risk of encirclement.

“A decision was made to reinforce our group with the necessary forces and resources,” he said. He added that Ukrainian forces were retreating to more favorable defensive positions, which some commentators interpreted as a possible prelude to a complete withdrawal from Kursk.

Russian military analysts said a withdrawal was likely to merely shift the battle to Ukrainian territory, pitting Kyiv’s forces in the Sumy region that borders Kursk against tens of thousands Russian soldiers and their North Korean allies.

Sanjana Varghese, Marc Santora and Michael Schwirtz contributed reporting.