On Wednesday morning, Toropets authorities said buses had already been prepared for the evacuation.
They also claimed that the situation was “under control” in the town of about 13,000 residents.
The authorities did not say how many people were being evacuated.
Meanwhile, Russia’s state media reported that regional schools and kindergartens would be closed on Wednesday.
Overnight attacks were also reported in Russia’s western Bryansk, Kursk, Oryol and Smolensk regions.
Local officials said nearly 50 drones and two missiles were shot down.
Ukraine has not commented on the reported attacks.
Overnight, Ukrainian air defences were engaged against oncoming Russian drones near the capital Kyiv, city military administration head Serhiy Popko said.
There were also reports of blasts in Ukraine’s north-eastern city of Sumy, near the Russian border.
It was not immediately clear whether there were any casualties.
The claims by both Russian and Ukrainian officials have not been independently verified.
Russian President Vladimir Putin launched a full-scale invasion of Ukraine in February 2022.
