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.