The incursion launched on August 6 from northeastern Ukraine into Russia's Kursk region caught Moscow off guard and boosted the morale of Ukrainians exhausted more than two years into Russia's invasion.
Kyiv said one of the aims of the offensive -- the largest by a foreign army on Russian soil since World War II -- was to divert Moscow's forces from fighting in eastern Ukraine.
"Perhaps the enemy pulled away from some other directions, perhaps from the reserves, but we did not feel any significant changes here," said Oleksandr, a soldier deployed near Toretsk.
"If this is a short-term operation, it will strengthen us," said Bogdan, a serviceman sitting at a cafe in Druzhkivka.
"If it's a long-term operation and we plan to stay in Kursk, it will deplete our main resources."
Russian offensive 'accelerating'
Ukrainian President Volodymyr Zelensky congratulated soldiers who have "proven that they can push the war into Russia" in a message on Sunday marking two months since the operation began.
Zelensky says the Kursk offensive had slowed down Russian advances in eastern Ukraine.
But data supplied by the Institute for the Study of War and analysed by AFP shows Moscow made its biggest monthly gains since October 2022, advancing on 477 square kilometres (184 square miles) of Ukrainian territory in August.
Russian troops seized the city of Vugledar earlier this month, and are approaching Pokrovsk, a former logistics hub.
"The Russian army's offensive is accelerating -- at the cost of heavy losses -- we can't say that the Kursk offensive has fulfilled its goals," said Yohann Michel, a French military expert and Research Fellow at the IESD Lyon.
The offensive only "showed something is possible with the Ukrainian armed forces and that it is possible to enter Russia without it causing an apocalypse", he added.
'Beautiful' picture
For many Ukrainian soldiers, the Kursk offensive is still a source of pride.
Sergiy, a soldier just back from Kursk, said the morale and political gains were worth the gamble.
Ukraine captured scores of Russian conscripts in the Kursk region who can help Kyiv get its prisoners of war back.
And the Kursk operation, Sergiy said, created "a beautiful propaganda picture that Ukraine can conquer and conduct offensive operations".
That signal was important to Ukraine's exhausted population and servicemen.
"I think that this particular country (Russia) should go through everything that it has done in our country," said another soldier named Sergiy from the 43rd brigade.
"At the same time, we don't do any of the horrible things that the soldiers of the Russian Federation have done, are doing, and continue to do," he said.
Dmytro, an artilleryman from the same brigade, said he was jubilant when he watched his fellow soldiers pour into Russia, hundreds of kilometres away from the Donbas region where he was posted.
"I just felt pride for our soldiers, that they had the inspiration to fight the enemy on its territory. Russia, which invaded our country, will feel the same as us and will see what war is," he said.
What next?
The operation also aimed to show Ukraine's Western backers, who have been dragging their feet in providing more aid, that their support can have a visible impact.
Kyiv's main ally, the United States, will soon hold elections that could carry Ukraine-sceptic Donald Trump back to the White House.
If Ukraine had to enter negotiations, holding a slice of Russian territory could improve its position.
But the prospect of any talks seems a distant one.
"Is this operation a success? Militarily, not really. The morale gains are temporary and fading," said Olivier Kempf, an associate fellow at the Foundation for Strategic Research.
"It makes sense given negotiations... but if you don't have negotiations in mind, it's completely absurd."
And, paradoxically, Russia could gain from keeping Ukrainian troops away from the main front in eastern Ukraine.
"Russia can turn this initial setback into a real strategic asset," said Kempf, who also heads the strategic research firm La Vigie.
Near the eastern front, some worry that Ukraine could get bogged down in Kursk.
"Now the question is what we do next," said one soldier, who wished to remain anonymous.
"Where will we get the people, the strength and the means to continue this story or somehow complete it? God knows how this story will end."
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