The Russian Defence Ministry has said that it brought down three Ukrainian drones over the Belgorod region, while the regional governor said that one man had been killed in a Ukrainian rocket strike on a village close to the border.
Separately, the governors of the nearby frontier regions of Bryansk and Kursk said a string of border villages had come under fire from Ukraine, and a woman had been wounded in Kursk region.
Ukrainian drone attacks on Russian territory have picked up in recent weeks, with dozens of drones striking Russia at once on some days, reaching as far as the western city of Pskov, 600km from Ukraine.
Russian-installed authorities in the Moscow-controlled part of Ukraine's Kherson region also said on Saturday that Kyiv struck the village of Maslivka in a drone strike, wounding a civilian.
Meanwhile, the Nobel Foundation said it would not invite the ambassadors of Russia, Belarus and Iran to attend the Nobel Prize awards ceremony in Stockholm this year after all, reversing an earlier decision after widespread criticism.
Last year, the foundation left out the ambassadors of Russia and its ally Belarus because of Moscow's invasion of Ukraine.
The foundation said on Thursday it would invite them, and Iran's ambassador, to this year's prize award ceremonies in December, commenting that it sought to include even those who did not share the values of the Nobel Prize.
That announcement prompted the leaders of several Swedish political parties to say they would boycott the ceremonies.
"We recognise the strong reactions in Sweden," the foundation said in a statement.
"We, therefore, choose to repeat last year's exception to regular practice - that is, to not invite the ambassadors of Russia, Belarus and Iran to the Nobel Prize award ceremony in Stockholm."
The prizewinners are announced in early October and five of the six Nobel prizes are awarded in Stockholm every year after a nomination process that is kept secret for the next 50 years.
The Nobel Peace Prize is awarded in Oslo where separate festivities are held.