Kyiv hopes that the surprise incursion into Russia, which started on August 6, will change the dynamic of the more than two-year-old conflict.
More than 3,000 people have been evacuated over the last 24 hours from areas in Russia's western Kursk region affected by the ongoing incursion of the Ukrainian army.
The Russian Emergency Ministry said on Saturday that more than 10,000 local residents were staying at temporary accommodation centres in other parts of the country.
The incursion, which Russian authorities say has led to the evacuation of more than 120,000 civilians, came as a shock to many people living in the Kursk oblast which borders Ukraine.
"No one expected that this kind of conflict was even possible in the Kursk region," said Yan Furtsev, a member of the local opposition party, Yabloko.
"That is why there is such confusion and panic, because citizens are arriving (from front-line areas) and they’re scared, very scared."
A daring Ukrainian military push into Russia’s Kursk region has seen Kyiv's forces seize several villages, take hundreds of prisoners and force the evacuation of tens of thousands of civilians in what has become the largest attack on Russia since World War II.
In more than a week of fighting, Russian troops are still struggling to drive out Ukraine's forces.
Kyiv hopes that the surprise incursion into Russia, which started on August 6, will change the dynamic of the more than two-year-old conflict.
But Ukrainian officials have repeatedly said that the aim of the operation is not to occupy Russia.
"Ukraine is not interested in occupying Russian territories," one of Zelenskyy's senior aides, Mykhailo Podolyak, said on X on Friday.
"In the Kursk region, we can clearly see how the military tool is being used objectively to persuade Russia to enter a fair negotiation process," he said.