President Vladimir Putin says the Ukraine is trying to undermine Russian stability with its incursion into the south of the country, but it will not succeed.
"The losses of the Ukrainian armed forces are increasing dramatically for them, including among the most combat-ready units, units that the enemy is transferring to our border," Putin told a televised meeting on Monday with top security officials and regional governors.
"The enemy will certainly receive a worthy response, and all the goals facing us will, without a doubt, be achieved."
Putin said it appeared that Ukraine was trying to improve its negotiating position in the war, but that there could be no question of negotiations with an enemy he accused of targeting civilians in its operation in the Kursk region.
He said Ukraine was trying to slow Russia's advance on other parts of the battle front, but that Moscow's forces were still advancing.
Earlier Ukrainian President Volodymyr Zelenskiy said the incursion into Russia's Kursk region was to "restore justice" and pressure Moscow's forces.
Moscow's forces were in their sixth day of intense battle against Kyiv's largest incursion into Russian territory since the start of the war, which left southwestern parts of Russia vulnerable before reinforcement started arriving.
Russia on Monday evacuated civilians after Kyiv increased military activity near the border just days after its biggest incursion into sovereign Russian territory since the start of the 2022 war.
Ukrainian forces rammed through the Russian border last Tuesday and swept across some Western parts of Russia's Kursk region, a surprise attack that may be aimed at gaining leverage in possible ceasefire talks after the US election.
Apparently caught by surprise, Russia by Sunday had stabilised the front in the Kursk region, though Ukraine had carved out a sliver of Russian territory where battles were continuing on Monday, according to Russian war bloggers.
In the neighbouring Belgorod region to the south, regional governor Vyacheslav Gladkov said evacuations had begun from the Krasnaya Yaruga District due to "enemy activity on the border".
"I am sure that our servicemen will do everything to cope with the threat that has arisen," Gladkov said. "We are starting to move people who live in the Krasnaya Yaruga district to safer places."
Russia has imposed a tight security regime in the Kursk, Bryansk and Belgorod regions while its ally Belarus said it was bolstering its troop numbers at its border after Minsk said Ukraine had violated its airspace with drones.
Russian officials say Ukraine's attacks on Russian sovereign territory are aimed at showing its Western supporters that Kyiv can still muster major military operations while trying to gain a bargaining chip ahead of possible ceasefire talks.
Russia invaded Ukraine in February 2022 in what the Kremlin calls a "special military operation" and now controls 18 per cent of Ukrainian territory. Russian forces, which have a vast numerical supremacy, have been advancing this year along the 1000km front after the failure of Ukraine's 2023 counteroffensive to make any major gains.
The Ukrainian attack has prompted some in Moscow to question why Ukraine was able to pierce the Kursk region so easily after more than two years of the most intense land war in Europe since World War II.
The war bloggers said Ukrainian forces in Kursk were trying to encircle Sudzha, where Russian natural gas flows into Ukraine, while major battles were underway near Korenevo, about 22km from the border, and Martynovka.
"The situation on the borders of the western Belgorod region is alarming," said Yuri Podolyaka, an influential pro-Russian military blogger, adding that Ukraine was probing the border at several places.
"The enemy has three fairly large groupings here."
