Five months after Ukrainian forces crossed the border in the first ground invasion of Russia since World War II, the two armies are engaged in some of the fiercest clashes of the war there, fighting over territory and influence in the conflict.

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

The fighting in Russia’s Kursk region has taken on a layer of significance for the territory’s potential to play a role in any ceasefire talks. Faced with the prospect of an unpredictable new US president — who has promised a quick end to the war, without clarifying the terms — Ukraine hopes to use Russian territory as a bargaining chip.

Russia, relying on North Korean reinforcements, hopes to expel that territory from Ukraine.

Here, the Russians need to take this territory at all costs and are putting all their strength into it, while we are doing our best to keep it, said the sergeant. Oleksandr, 46, Ukrainian infantry platoon leader. “We hold on, we destroy, we destroy, we destroy — so much so that it’s hard to even understand.”

He and other soldiers, who asked to be identified only by name or call sign in accordance with military protocol, said waves of attacks by North Korean infantry have made the battles far more fierce than before.

“The situation got much worse when the North Koreans started arriving,” said Jr. Oleksii, 30 years old, platoon leader. They press our fronts en masse, find weak points and break through them.

Russia, with the help of an estimated 12,000 North Koreans, has retaken about half of the territory it lost over the summer. Its attacks over the past week have further eaten away at territory held by Ukraine.

But Ukrainian forces have also gone on the offensive in recent days, seeking to secure an area west of Sudzha, a town in Russia about six miles from the border that has become an anchor for Ukrainian forces, which in August captured about 200 square miles.

“If they keep pressing us and we don’t push back, the enemy will have a sense of superiority,” said Andrii, 44, a military intelligence officer. “When someone keeps hitting you and you don’t hit back, the attacker will feel psychologically comfortable, even relaxed.”

The Russians have largely thwarted the attack, but fighting continues and the situation remains unpredictable, the soldiers said.

The intensity of the fighting could be seen on the road approaching the Russian border: a steady stream of tanks, armored personnel carriers and other vehicles rolled past broken and blown-up equipment.

Russian bombs and rockets exploded with thunderous force in border villages, and Ukrainian missiles could be seen flying across the sky in the opposite direction.

Tens of thousands of drones were also hunting targets. They have transformed the battlefieldalthough Ukraine has improved its electronic warfare capabilities, limiting the effectiveness of drones that rely on radio signals. Russia has now flooded the theater with drones guided by ultra-thin fiber optic cables, with a flight range of more than 10 miles.

The best current defense against them is a shotgun, Ukrainian soldiers said.

The renewed fighting is taking place against a deeply uncertain political background. US President-elect Donald J. Trump spent months on the campaign trail questioning US military aid to Ukraine. He said he wanted to end the war quickly, but did not indicate how.

Russian forces have been on the offensive for more than a year in eastern Ukraine, constantly progressing despite incredible losses.

With its incursion, Ukraine aims to create a buffer zone to protect hundreds of thousands of civilians in the city of Sumy, less than 20 miles from the Russian border. Ukraine also wants to relieve pressure on the eastern front by drawing the Russians back to their country.

President Volodymyr Zelensky said the campaign sent a strong message to the world that Ukraine can do more than defense.

“It is one of our victories, I think one of the biggest victories, not only last year, but during the whole war,” said Mr. Zelensky on Thursday in Germany, while meeting with representatives of countries that provide military support to Ukraine.

Still, some military analysts warn that Ukraine’s Kursk campaign could see its forces stretched further and losing ground in its own eastern Donbass region.

Many soldiers fighting in Kursk believe the painful losses in eastern Ukraine would have been worse without their campaign.

“We have to understand that the Russians are using their most elite soldiers and their best reserves in this area,” said Capt. Oleksandr Shyrshyn, 30, a battalion commander in the 47th Mechanized Brigade. “Considering what they could be doing in other parts of Ukraine, that’s good.”

He was still bleary-eyed after the battle a few days earlier in thwarting a major Russian attack.

The Russians attacked the Ukrainian positions in six waves, using more than 50 tanks, armored personnel carriers and other vehicles.

While dozens of enemy soldiers were killed and wounded and a large amount of Russian equipment destroyed, Capt. Shyrshyn said, the Russians advanced several miles.

“When the first wave comes, we focus on it, deal with it, and then the next one comes,” he said. There is no time to divert artillery or other resources while the next wave comes from the other line of attack.

“We’re behind,” he said. “Then the next wave comes, and one of them manages to reach the required section and complete his task.”

It remains difficult, he said, to see how many in the West view the war in Ukraine as a video game and refuse to see the threat Russia poses to the world.

He acknowledged the decline in Ukrainian morale during nearly three years of war, but said most soldiers still understood why they had to fight. “Stopping it will mean our death, that’s all,” he said.

North Korea’s entry into the war, some Ukrainian soldiers said, should alarm European nations and their allies.

North Korean troops fought as a disciplined, committed and fearless force, they said, usually moving in large formations on foot, even through minefields while under heavy artillery fire and escorted by drones. Ukrainian authorities announced on Saturday that their forces captured two North Korean soldiers and that they were the first to be taken alive so far.

Sergeant Oleksandr, a platoon leader, said the carnage in Kursk was as terrifying as anything he had witnessed since joining the army in 2014.

“You look and you can’t fully understand where you are, seeing every day how many people we destroy,” he said.

He compared it to Bakhmut, when machine gunners had to be replaced regularly because they couldn’t handle the pace of killing. “After two hours of laying so many people, they couldn’t take it mentally,” he said.

“It’s the same here now,” he said, sharing cellphone footage showing the aftermath of the recent attack. The field was littered with bodies, torn and twisted and piled up in ways that made it difficult to count the dead.

“It’s worst for the infantry,” he said. “When you’re sitting there and they’re coming at you, and everything’s flying at you.”

Anastasia Kuznetsova contributed reporting.