Ukrainian President Volodymyr Zelenskyy has acknowledged that his country's military has been carrying out attacks in western Russia since Tuesday.

In a video address on Saturday, Zelenskyy said, "Today Commander-in-Chief Syrskyi has already reported several times - on the frontline situation and on our actions to push the war out into the aggressor's territory."

Russia's defense ministry said it sent reserve units and beefed up its airpower to repel Ukraine's cross-border attacks, and claimed it blocked the attempt to intrude deeper into Russian territory.

The ministry also said it destroyed 14 Ukrainian drones and four ballistic missiles in the western Kursk region, where the Ukrainian military is carrying out operations.

The region's acting governor Alexei Smirnov said on social media on Sunday that 13 people were injured in a building in Kursk which was struck by debris from a Ukrainian missile. He called the Ukrainian military terrorists.

Russia's ministry of emergency situations said that more than 76,000 people have already evacuated from the border areas in Kursk region to neighboring regions, including Moscow and Tula.

Meanwhile, Russian forces are continuing attacks. Ukraine's State Emergency Service said on Sunday that a 35-year-old man and his 4-year-old son were found dead under the rubble of a building hit by Russian rocket fragments. It said three others, including a 13-year-old child, were seriously injured.