Ukraine claims it now controls over 1,000 square kilometres of Russian territory, as it continues to advance .
It's the most significant advance into Russian territory since Russia began its full-scale invasion of Ukraine in February 2022.
Russian President Vladimir Putin has described the attack as "a major provocation" and said it was aimed at improving Ukraine's negotiating position in potential peace talks.
Ukrainian President Volodymyr Zelenskyy has said the cross-border offensive is "purely a security issue" that aims to capture "areas from which the Russian army struck at our Sumy region".
The area Ukraine now controls within Russia, according to the Institute for the Study of War, a US research group and think tank. Source: SBS News
However, Russian officials said that Ukraine's incursion was only about 12km deep and 40km wide — less than half the size of the area that Kyiv claims it occupies.
The non-profit, United States-based think tank the Institute for the Study of War has estimated that Ukraine controls at least 800 square kilometres of territory in Kursk.
Even if Ukraine's claim of having seized 1,000 square kilometres of Russia is correct, that's less than 0.006 per cent of Russia's total landmass of roughly 17,125,191.
Meanwhile, Russia remains in control of around 20 per cent of Ukraine.
While Ukraine says it controls a tiny amount of Russian territory, Moscow has occupied over 20 per cent of Ukraine. Source: SBS News
Putin told a televised meeting with government officials that "one of the obvious goals of the enemy is to sow discord" and "destroy the unity and cohesion of Russian society".
Some 121,000 people have fled the Kursk region since the start of the fighting, which has killed at least 12 civilians and injured 121 more, regional governor Alexei Smirnov said during the televised meeting with Putin.
Authorities in Kursk announced on Monday they were widening their evacuation area to include a district with some 14,000 residents and the nearby Belgorod region also said it was evacuating a new border district.
Russia claims 12 civilians have been killed so far as Ukraine advances into the Kursk region, with over 100,000 more evacuating. Source: SBS News / Lilian Cao
"What do I think about Kursk? Bold, brilliant, beautiful. Keep it up," he told reporters.
The Ukrainian finance ministry recently said that, since February 2022, direct budget support from the United States had reached almost $27 billion, the largest source of financial assistance to Ukraine.
Putin has said Ukraine had received help from its "Western masters" and vowed that "the enemy will certainly receive a worthy response".
With additional reporting by Agence France Presse and the Reuters news agency.