Five months after Ukrainian forces swept across the border in the first ground invasion of Russia since World War II, the two armies are engaged in some of the most furious clashes of the war there, fighting over land and leverage in the conflict.

The intensity of the battles recalls some of the worst sieges of eastern Ukraine over the past three years, including in towns like Bakhmut and Avdiivka, names that now evoke memories of mass slaughter for soldiers on both sides.

The fighting, in the Kursk region of Russia, has taken on a layer of significance for the territory’s potential to play a role in any cease-fire negotiations. Facing the prospect of an unpredictable new U.S. president — who has vowed to end the war swiftly, without clarifying the terms — Ukraine hopes to use Russian territory as a bargaining chip.

Russia, relying on North Korean reinforcements, hopes to knock that territory out of Ukraine’s grasp.

“Here, the Russians need to take this territory at any cost, and are pouring all their strength into it, while we are giving everything we have to hold it,” said Sgt. Oleksandr, 46, a leader of a Ukrainian infantry platoon. “We’re holding on, destroying, destroying, destroying — so much that it’s hard to even comprehend.”

He and other soldiers, asking to be identified by only a first name or call sign in accordance with military protocol, said that waves of attacking North Korean infantry had made the battles far more ferocious than before.