In his nightly video address, Zelensky referred to the move as “our actions to push the war onto the aggressor's territory", the Reuters news agency has reported.
"Ukraine is proving that it can indeed restore justice and ensure the necessary pressure on the aggressor”, he added.
On Sunday, Moscow's forces have been in their sixth day of intense battles against Kyiv's largest incursion into Russia's western Kursk region since the start of the war, which left southwestern parts of Russia vulnerable before reinforcement started arriving.
In a sign of the gravity of the situation, Russia imposed a sweeping security regime in three border regions on Saturday.
Russia's TASS state news agency wrote that more than 76,000 people had been evacuated from the affected area.
Russian military authorities said the attacks had been halted, but Russia has not so far pushed the Ukrainian forces back over the border.
Russian military bloggers said the situation had stabilized after Russia's reinforcements, though they said Ukraine was swiftly building up forces, Reuters reported.
The bloggers also claimed fighting is taking place as deep as 20 km inside the Kursk region, according to Reuters.
Russia's nuclear agency Rosatom on Saturday said Ukraine's shock cross-border attack posed a "direct threat" to a nuclear power plant located less than 50 kilometres from the combat zone.
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Source: Reuters
