Ukraine, according to Zelensky on Saturday night, is advancing the conflict into the "territory of the invaders."
After an unexpected offensive on Tuesday, Kiev has penetrated into Russia by more than ten kilometres.
The Kursk region's border areas have reportedly seen 76,000 people evacuated, according to Russian claims.
Since Russia began its full-scale invasion of Ukraine in February 2022, this is the biggest encroachment into the country.
According to local officials, Russian drone and missile attacks occurred immediately over Kyiv and several other places.
After a missile component fell on residential homes in the Kyiv region, a 35-year-old man and his four-year-old son died.