Five months after storming across the border into the Kursk region of southern Russia, Ukrainian forces resumed their offensive on Monday to push deeper into Russia, although they appear to have lost a strategic city in eastern Ukraine.

While the scale of the renewed Ukrainian offensive in Kursk remains unclear, both Russian and Ukrainian officials reported heavy fighting Sunday night. Combat footage geolocated by military analysts shows that Ukraine is trying to break through Russian defenses in at least three directions.

It is the first significant attempt by Ukrainian troops to advance in Kursk since the original invasion in August. Since then, Russia has regained about half of the territory it lost.

At the same time, Russia’s Defense Ministry claimed on Monday that its forces had taken control of Kurakhov, an important but devastated industrial city, drawing closer to Ukrainian forces in the southern Donbass region after more than two months of light bombardment and heavy fighting.

Ukraine’s military command in the east did not comment on Russia’s claim that Kurakhove had fallen. Soldiers fighting in the area and a local Ukrainian military official said when reached by phone that while there were pockets of resistance in factories on the outskirts, the city was essentially lost. They requested anonymity to discuss sensitive military information.

In a statement, the Kremlin said its Defense Minister Andrey Belousov congratulated Russian soldiers on capturing the city on Monday,

The fall of Kurakhove and surrounding cities could allow Russia to expand its own attack on the city of Pokrovsk21 miles north, military analysts said.

Russian forces are trying to surround Pokrovsk, a focal point war in recent months, from the south, hoping to avoid brutal and protracted urban fighting. They advanced to within about a mile of a vital supply road southwest of the city, according to several analysis groups, including the Institute for the Study of War, a Washington-based think tank.

Despite the fact that both sides were beaten and exhausted after almost three years of war, the fighting at the front only intensified.

The dual offensives — with the Ukrainians attacking, albeit modestly, Kursk and the Russians continuing to attack eastern Ukraine head-on — underscored how both the Kremlin and Kiev want to show strength as President-elect Donald J. Trump prepares to take office, analysts said.

Mr. Trump has promised to end the war quickly without saying how.

In a three-hour conversation with podcaster Lex Fridman, President Volodymyr Zelensky expressed his belief that Mr. Trump can fulfill that promise.

“I think President Trump not only has the will, he has all these capabilities, and it’s not just talk,” he said. “I really count on him and I think our people really count on him, so he has enough power to press him, to press Putin.”

The appearance with a podcaster popular in Trump circles — including Elon Musk, who highlighted the interview on his social media network, X — appeared to be an attempt to communicate directly with Trump supporters.

Mr. Zelensky also reaffirmed his belief that there can be no lasting peace unless Ukraine is militarily strong and supported by the United States.

“If we don’t have security guarantees, Putin will come again,” he said.

Antony J. Blinken, the US secretary of state, echoed those concerns during a trip to South Korea on Monday.

“At some point there will be a ceasefire. “It will not be ‘game over’ in Putin’s mind,” said Mr. Blinken to journalists. “His imperial ambitions remain, and what he will seek to do is rest, reorganize and eventually strike again.”

Mr. Blinken also said that Ukraine’s Kursk campaign would play a key role in any peace talks.

“The positions of the Ukrainian armed forces in the Kursk region are very important,” he said, “because, of course, this is something that will be relevant to any negotiations that may take place next year.”

North Korea has sent more than 11,000 troops to fight alongside the Russians in Kursk, Ukrainian and American officials said, and Mr. Blinken said the partnership between the two countries continues to grow. He repeated previous claims that Moscow was willing to supply North Korea with advanced space and satellite technology in exchange for weapons and equipment to help its war effort in Ukraine.

Despite bringing North Korean troops into the Battle of Kursk, Ukraine has managed to hold on to more than 150 square miles of land inside Russia – just under half the territory it initially captured.

However, the amount of territory Ukraine holds inside Russia is less important than the message the campaign sends to the world, military analysts said.

“Kursk is a strategic shift in the narratives of war,” said Taras Chmut, a former military officer and chief Come back alivea charity that supports the Ukrainian military. “It’s about Russia losing territories, its own territories. It is about Ukraine being able to implement some unexpected actions and unconventional asymmetric approaches.”

But Ukraine’s renewed Kursk offensive comes as it struggles to stabilize defensive lines.

The loss of Kurakhov, which covers only about three square miles of the country, highlighted problems with the way Ukraine manages and deploys its forces, Ukrainian analysts and soldiers said.

Under pressure to address those concerns, Ukraine’s defense minister, Rustem Umerov, ordered a comprehensive review of the military command.

“Winning requires a deep analysis of experience and an honest understanding of mistakes,” he said in a statement Thursday.

The problems run deeper than a simple lack of personnel, analysts and soldiers said in interviews over the past year.

“When undermanned brigades lose positions, it is not always due to insufficient recruitment,” Ukrainian think tank Frontelligence wrote in a report published on Friday.

“Poor organizational decisions are often to blame, such as directing new recruits to new units instead of bolstering depleted veteran brigades.”

The report added: “The window of opportunity to address these identified issues is closing rapidly, and inaction is not an option.”

AND sharp report by Ukrainian journalist Yury Butusov about the newly created 155th Anne of Kyiv Brigade, which was trained in France and equipped with Western weapons, raised concerns about problems in the Ukrainian military and helped fuel calls for urgent change.

The State Bureau of Investigation opened a criminal case in December into the management of the brigade, which has experienced high levels of desertion and problems related to personnel and management.

Russia also faces tough challenges, even if they remain hidden from the public, military analysts say. The Kremlin maintains tight control over information and dissent is punished, but has yet to achieve an operationally significant breakthrough despite its superiority in manpower and weaponry.

During 2024, Russia occupied 4,168 square kilometers — or about 1,600 square miles — of territory, mostly fields and small villages, the Institute for the Study of War reported.

Although Russian forces have recently advanced as fast as at any time since the early months of the war, the research group said it would still take more than two years at their current rate of advance for the Russians to capture the rest of the Donetsk region in eastern Ukraine is still under under the control of Ukraine.

Ljubov Soludko contributed reporting.