Russian President Vladimir Putin earlier accused Ukraine of carrying out a “serious provocation.”
Ukrainian officials have remained largely silent about the attack. The exact situation on the ground is hard to determine, and neither side has released specific details.
The Ukrainian president did not directly comment on the attack on Thursday, but said “everyone can see how the Ukrainian military can carry out a surprise attack and achieve results.”
The International Atomic Energy Agency (IAEA) said it was monitoring the Kursk nuclear power plant, according to Russian state news agency RIA-Novosti.
The Russian Defense Ministry said on Thursday that its military was “continuing to destroy” Ukrainian armed units using air strikes, rocket attacks and artillery fire.
The Defense Ministry said Russian reserves had been rushed to the area.
The Institute of War, a prominent think tank, said geolocation-based imagery showed Ukrainian armored vehicles advanced as far as 10 kilometers (6.2 miles) into the Kursk region during the first two days of the invasion.
The Russian military leadership is under strict surveillance domestically. Some popular and generally well-informed pro-war Telegram channels say the situation on the ground is not as stable as the Kremlin suggests.
The influential pro-war channel Rybar Telegram on Wednesday harshly criticized the Russian military's top brass, saying “all information was transmitted to the useless headquarters for two months”, adding that there was “enough time to make an appropriate decision.”
Leaders of the Kursk region in Russia and Ukraine told residents to leave for their own safety.
On Wednesday, the head of Ukraine's Sumy region, Volodymyr Artyukh, ordered the evacuation of areas bordering Kursk.
The governor of Russia's Belgorod region, Vyacheslav Gladkov, said on Thursday that settlements across his region had come under attack by Ukrainian troops in the past 24 hours.
