Ukrainian forces may be attempting to break through the border into Russia's Belgorod Oblast, regional governor Vyacheslav Gladkov claimed on Aug. 27.
Kyiv has not commented on the claims, which could not be independently verified.
The statement comes as Ukraine's cross-border incursion into neighboring Kursk Oblast reaches its three-week mark. Belgorod Oblast is lodged between Russia's Kursk and Voronezh regions and borders Ukraine's Sumy, Kharkiv, and Luhansk oblasts.
"There is information that (Ukraine) is attempting to break through the border of Belgorod Oblast," Gladkov wrote on his Telegram channel.
"According to the Russian Defense Ministry, the situation on the border remains difficult but under control."
Reports of the alleged attacks have also emerged on Russian Telegram channels.
According to the Mash channel, roughly 200 Ukrainian troops have attacked the border crossing at Nekhoteyevka and another 300 at Shebekino.
Another channel, Shot, claimed that Ukrainian forces had been pushed back from Nekhoteyevka after suffering losses and claimed that no clashes had taken place at Shebekino.
Shot pointed out that the front near Shebekino, which lies just across the border from the embattled Ukrainian town of Vovchansk, has been pushed further south after Russia launched its offensive into Kharkiv Oblast in May.
Nekhoteyevka also lies at the border of Ukraine's Kharkiv Oblast, some 6 kilometers (almost 4 miles) from the Ukrainian settlement of Kozacha Lopan and around 30 kilometers (almost 20 miles) north of Kharkiv.
There have been multiple signs that Ukraine's incursion into Kursk Oblast is spilling over to Belgorod Oblast. A unit of the Ukrainian 252nd Battalion appeared to have entered the village of Poroz on Aug. 10.
Russia also claimed that Ukraine unsuccessfully attacked the Kolotilovka border checkpoint on Aug. 12.
Previously, Shebekino became a key flashpoint during a cross-border incursion carried out last year by anti-Kremlin militias fighting on Ukraine's side.
Dmytro Basmat
