Russia has started moving some residents from the city of Belgorod following deadly attacks by Ukraine.
On Friday, governor Vyacheslav Gladkov said several families had left the city - which is close to Ukraine's border.
Last weekend, 25 people were killed and more than 100 injured in one of the deadliest attacks on Russia since it invaded Ukraine in February 2022.
The attack followed a recent huge wave of Russian strikes on Ukraine, which killed dozens and injured over 160.
Those strikes were described by Kyiv as Russia's biggest missile bombardment of the war so far.
Writing on Telegram on Friday, Mr Gladkov said he had seen appeals on social media by people saying, "We are scared, help us get to a safe place."
"Of course we will! We have already moved several families," he said.
The governor said residents would be taken to the towns of Stary Oskol and Gubkin where they could stay "for as long as necessary".
However, he said not everyone could be accommodated there, so he would ask colleagues from other regions to help.
The governor later posted a warning of a possible missile attack and urged residents to head home or into shelters.
Russia has repeatedly accused Ukraine of being behind drone strikes in recent months.
Kyiv rarely admits to such attacks across the border, although it has carried out such strikes before.
The cross-border fire comes as the US accuses Russia of a "significant and concerning escalation" in Ukraine, with the use of ballistic missiles and launchers supplied by North Korea.
Moscow has denied any such collaboration.
The last US military aid package to Ukraine, worth some $250m (£195m), was approved by the White House on 27 December.
Talks on further funding have stalled in Congress because of a lack of support among Republicans, who insist that tougher security measures on the US-Mexico border must be part of any military aid deal.
Ukraine has warned that its war effort and the country's public finances are at risk if further Western aid does not come soon.
