President Volodymyr Zelensky acknowledged for the first time on Saturday that Ukrainian forces were fighting in Russia's Kursk region and said the operation was part of Kyiv's drive to restore justice after Russia's 2022 invasion.
Russia said Ukrainian forces pushed into Kursk region last Tuesday and Russian military bloggers have acknowledged they made some headway, while saying the situation had since stabilised.
Zelensky had previously stayed silent about the operation.
In his nightly video address, the president said he had discussed the operation with top Ukrainian commander Oleksandr Syrskyi, while not forgetting the battles troops face on the difficult eastern front.
"Today, I received several reports from commander-in-chief Syrskyi regarding the front lines and our actions to push the war onto the aggressor's territory," he said.
"I am grateful to every unit of the defence forces for ensuring that. Ukraine is proving that it can indeed restore justice and ensure the necessary pressure on the aggressor."
Zelensky had previously alluded to the operation, praising the military's ability "to surprise" and thanking them for taking Russian soldiers prisoner to be used in future negotiations, specifically referring to the past week.
In paying tribute to Ukrainian forces along the 1,000-km (600-mile) front line, Zelensky made special mention of actions in northern Sumy region, across the border from Russia's Kursk region.
Russia has stepped up its attacks of guided bombs and other aerial strikes in Sumy, prompting mass evacuations.
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