Russia said Wednesday that another person was killed in Ukrainian attacks on its Belgorod region, as President Vladimir Putin vowed to restore security in the country's border areas.

Ukraine has shelled the Belgorod region for months but last week stepped up attacks ahead of Russia's presidential election.

Anti-Kremlin Russian fighters also claimed several incursions last week on Russian border regions.

"According to preliminary information, one person died," Belgorod governor Vyacheslav Gladkov said on social media.

"The man was in the car when it was hit by shrapnel and died of his wounds at the spot before the ambulance arrived," Gladkov said.

In Moscow, Putin promised to restore safety in Russia's border regions and said his inevitable win in a weekend presidential vote was a "prologue" to victory in Ukraine.

He spoke inside the Kremlin's gilded Andreyev Hall, addressing election officials after winning a fifth term in office in a vote with no genuine opposition.

"We will do everything to support people who lost their businesses and homes, we will do everything possible," Putin said.

"But the first thing, is of course to ensure security. There are different ways, they are not easy, but we will do them," he added, without elaborating.

"Victory in the elections is just a prologue to those victories that Russia so badly needs and that will definitely come," Putin said, two years into the Ukraine offensive.

He praised the "bravery of the people of Belgorod".

Gladkov also said Wednesday that schools in some border areas would shift to remote learning, a day after saying around 9,000 children would be evacuated from the region.