Fresh strikes Saturday in the Russian border region of Belgorod adjoining Ukraine killed two people, the regional governor said, as Moscow accused Kyiv of stepping up attacks during the ongoing presidential election.

"Very sad news, two people died, a man and a woman," said Vyacheslav Gladkov on Telegram, adding that eight rockets had been downed by Russian forces in the region.

He said the man died when a truck he was in was hit while the woman died in a parking lot. Her son was seriously injured and doctors "are battling to save his life", Gladkov said.

Two others were injured.

Russia's defence ministry earlier said it had downed rockets, missiles and drones in the border regions of Belgorod and Kursk. 

Russian leader Vladimir Putin on Friday promised a harsh response to waves of fatal Ukrainian aerial attacks on Belgorod and Kursk that have also seen fierce fighting in recent days with pro-Kyiv sabotage groups. 

"These strikes by the enemy do not and will not go unpunished," the long-time Russian leader said in comments aired on state-run television.