[Video transcript]
Hoping to fend off Ukrainian troops ...
Russia's Defence Ministry says this footage shows Ukrainian armoured vehicles being destroyed as heavy fighting along the border enters its third day.
Around 1,000 Ukrainian troops rammed through the Russian border two days ago into the Kursk region with tanks and armoured vehicles.
Heavy fighting was reported near the town of Sudzha, where Russian natural gas flows into Ukraine, raising concerns over a potential stop to transit flows to Europe.
Ukraine has released video footage allegedly showing Russian guards surrendering at a border crossing point in Kursk.
In his evening address, President Volodymyr Zelenskyy suggested Russia should get a taste of its own medicine, without referring directly to the incident.
Ukrainian President Volodymyr Zelenskyy: "Russia brought the war to our land, and should feel what it has done. We want to achieve our goals as soon as possible, in peacetime, under the conditions of a just peace. And it will be."
Kursk has declared a state of emergency and thousands of people are being evacuated.
Former Russian president Dmitry Medvedev has reacted to the incursion on Telegram and called for a further invasion of Ukraine.
"This is no longer just an operation to reclaim our official territories and punish the Nazis. It is possible and necessary to enter the territory of the still existing Ukraine. To go into Odesa, Kharkiv, Dnipro, Mykolaiv. To go into Kyiv and further. There should be no restrictions in the sense of any recognized borders of the Ukrainian Reich."
Moscow has been forced to call in reserves to stop Ukrainian soldiers from pushing deeper into its territory.