The Russian Emergency Situations Ministry released footage on Wednesday of people boarding buses in Rylsk and Lgovsk, in the Kursk region.
Regional authorities had already ordered the evacuation of several other areas.
Acting Kursk regional governor Alexei Smirnov said late Wednesday that security services, military personnel and local authorities would coordinate the evacuation of residents from the Glushkovo area on the border with Ukraine.
About 8,000 people from the Kursk region have been accommodated in temporary shelters in several Russian regions, the ministry said in a statement.
About 121,000 people have been evacuated from Kursk or fled the areas affected by the fighting on their own, authorities added.
Ukraine’s surprise charge onto Russian soil, which began on August 6, has shaken the Kremlin.
The audacious Kursk operation is the largest attack on Russia since World War II and could involve up to 10,000 Ukrainian troops backed by armor and artillery, military analysts say.
A state of emergency was declared in Kursk last Saturday.
