A Russian official in a southern region bordering Ukraine said on Sunday that thousands of people had crossed the border as Kyiv's army claimed to have pushed back Moscow's forces in the country's east.

"Over the past day, thousands of people have crossed the border. Most of them went to relatives in their own vehicles. Today, 1,342 people are being housed in 27 temporary accommodation centers in the region," Vyacheslav Gladkov, the governor of the Belgorod region, stated in a video statement on social media.

However, there has been no response from the Ukrainian side.