Ukrainian President Volodymyr Zelenskyy touted his country's nearly two-week-long incursion into Russia's Kursk region as a success on Monday, saying that the operation on the other side of the border was seeing opposing soldiers captured who could be exchanged for Kyiv's own troops.

"We are achieving our goals. In the morning, there is another replenishment of the exchange fund for our state," he said on the Telegram messaging service, referring to Russian soldiers taken prisoner by Ukraine.

The Ukrainian offensive in Kursk began on Aug. 6. Nearly two weeks later, Zelenskyy said, Ukrainian forces control more than 1,250 square kilometres of Russian territory and 92 settlements in the region.

Zelenskyy also said on Monday that his country's assault on Kursk showed that Kremlin threats of retaliation were a bluff, and he urged Kyiv's allies to loosen curbs on using foreign-supplied weapons.

Speaking to a gathering of Ukrainian diplomats, he singled out allies that have supplied long-range weapons but told Ukraine they cannot use them deep inside Russia for fear of crossing "red lines" set out by Russian President Vladimir Putin.

WATCH | Challenges for Moscow in Kursk:

Ukraine’s cross-border assault poses new challenges for Russia

Ukraine continues to hold and expand its control over Russian territory, nine days after it launched a surprise cross-border attack. Moscow says it will bring the incursion to an end, but there’s no sign of that happening yet.

"We are witnessing a significant ideological shift. The naive, illusory concept of so-called red lines regarding Russia, which dominated the assessment of the war by some partners, has crumbled apart these days," Zelenskyy said.

"If our partners lifted current restrictions on the use of weapons on Russian territory, we wouldn't need to physically enter the Kursk region to protect our border communities and eliminate Russia's potential for aggression," he said.

"But for now, we cannot use all the weapons at our disposal and eliminate Russian terrorists where they are."

Ukraine struggles to protect city

Despite its thrust into Russia, Ukraine's forces are on the defensive elsewhere. They face a battle to protect the strategic eastern city of Pokrovsk, where Russia has steadily advanced in recent weeks in heavy fighting more than two years since Russia's full-scale invasion in February 2022.

Ukraine's military said late on Monday its forces had fought 63 skirmishes over the course of the day against Russian forces on the Pokrovsk front, and it expected that area to remain the focus of Russian attacks.

Russia said a third bridge had been struck and damaged on the Seym River that winds through the Kursk region bordering northeastern Ukraine.

Ukraine has not yet commented on the strike, but Kyiv's air force chief has previously said his forces have destroyed two bridges to weaken enemy logistics.

Military analysts said the bridges were part of critical supply lines for Russian troops defending the area. Reuters could not independently confirm the damage to the bridges or the battlefield situation in Kursk.

Zelenskyy said on Sunday his troops were unleashing what he described as "maximum counteroffensive actions" aimed at creating a buffer zone and hurting Moscow's military potential.

More than 121,000 people have been evacuated from nine border districts in the Kursk region, Russia's emergencies ministry said.

Russian presidential aide Yuri Ushakov said Moscow was not ready to hold peace talks with Ukraine for now, given Kyiv's Kursk attack. Ukraine has demanded a full withdrawal of Russian troops from its territory before it sits down for any talks.

Ukrainian forces face a tough battle near Pokrovsk, a transport hub for Ukrainian forces. Russian troops are now about 10 kilometres from the outskirts of the city, said Serhiy Dobriak, head of the local military administration. He said up to 600 people were leaving on a daily basis and that municipal services could be cut off within a week as Russian forces close in.

Regional governor Vadym Filashkin said a curfew in settlements close to Pokrovsk had been tightened and that the situation was "very difficult."

Ukraine's top general said Kyiv was also "doing everything necessary" to defend the eastern city of Toretsk as Moscow tries to threaten Ukrainian supply lines. Russia said its forces had captured the nearby town of Zalizne.

Moscow to boost troops by year's end: official

The war, which has killed tens of thousands and devastated cities across Ukraine, shows no sign of letting up. Kyiv expects Moscow to boost its forces in Ukraine by year's end to 800,000, up from about 600,000 now, Ukraine's deputy defence minister, Ivan Havryliuk, told Ukrainian media.

Tim Mak, a Kyiv-based journalist covering the war in Ukraine on his newsletter The Counteroffensive, said it's possible that the events in Kursk could be beneficial for Moscow's standing with the public on the subject of the war.

Mak saw the possibility that "this occupation of part of Russian territory may rejuvenate the broader Russian public," he told CBC Radio's Front Burner in an interview that aired on Monday.

Ukraine has been backed by arms from its allies but is worried that support may drop as the all-out war grinds on.

German defence stocks fell on Monday after a newspaper said the Finance Ministry would not approve additional applications for Ukraine military aid because of budget constraints.

A ministry spokesperson later said Berlin was working intensively with its Group of Seven partners on a plan to make loans available for military support for Ukraine, funded by the proceeds of frozen Russian assets.