CNN — Ukrainian President Volodymyr Zelensky has confirmed Kyiv’s troops are fighting inside Russia, days into the surprise Ukrainian cross-border incursion into Russia’s Kursk region that has become a major embarrassment for the Kremlin.

“Ukraine is proving that it really knows how to restore justice and guarantees exactly the kind of pressure that is needed – pressure on the aggressor,” Zelensky said in his nightly address to the nation on Saturday, thanking “every unit” of Ukraine’s armed forces for making it possible “to push the war out into the aggressor’s territory.”

The statement marked the first time Zelensky officially acknowledged the incursion, which took by surprise both Russia and Ukraine’s allies. Ukrainian officials have for days remained tight-lipped about the operation, even as photographs, videos and firsthand reports of Ukrainian soldiers inside Russia started to emerge.

Moscow has been scrambling to contain the attack. Russian authorities imposed a sweeping counter-terror operation in Kursk and two other border regions and tens of thousands of people have been evacuated from Kursk.

Now into its sixth day, the attack on Kursk is a significant development in the more than two-year old conflict.