In his nightly televised address on Saturday, Zelensky said that the Ukrainian military is pushing the war "onto the aggressor's territory".
The statement marks Zelensky's first public acknowledgement of Ukraine's cross-border incursion into Russia's Kursk Oblast, which reportedly began on August 6 and has taken Russia by surprise, prompting mass evacuations across both sides of the border.
Zelensky thanked Ukraine's defence forces, and said he had discussed the operation in Russia with the country's senior military commander Oleksandr Syrsky.
Earlier, Russia had said that up to 1,000 Ukrainian troops, supported by tanks and armoured vehicles, entered the Kursk region on Tuesday morning.
Although Zelensky did not mention Kursk directly in his remarks, he acknowledged that the Ukrainian military is conducting an operation on Russian soil.