Some 11,000 people in the Belgorod region have been moved, Russian state media reported, because of “enemy action” near the border.
Belgorod lies next to Kursk – where Ukrainian troops launched their surprise attack into Russian territory last Tuesday.
Ukrainian forces have since advanced up to 18 miles (30km) inside Russia – the deepest incursion into the country since Moscow’s full-scale invasion of Ukraine. Kyiv claims thousands of troops are involved.
On Monday morning, residents of parts of Belgorod—which lies south of Kursk—were told not to panic but to evacuate.
Belgorod governor Vyacheslav Gladkov said people from the Krasnaya Yaruga district were being moved due to “enemy activity on the border.”
He also said the whole region was under a missile alert and told people to shelter in their basements.
However, he added that he was “sure that our servicemen will do everything to cope with the threat that has arisen.”
On Monday, people continued to be evacuated from Kursk, and thousands were told to leave their homes in the Belovsky district.
Belovsky governor Alexei Smirnov also issued a missile warning – saying people needed to take shelter in rooms without windows and with solid walls.
Temporary accommodation has been prepared, he said.
At the weekend, President Volodymyr Zelensky said Ukraine was taking the war into “the aggressor’s territory.”
He acknowledged the attack for the first time on Saturday night – saying Russia had launched 2,000 attacks from Kursk this summer and it deserved a response.