Getty ImagesUkraine said it hit a drone command unit in the Kursk region, amid reports of fresh attempts to cross into Russia.
Sunday's attack on the unit was located near the Russian village of Tyotkino, according to the Ukrainian general staff.
Russian officials also reported an electrical substation in the town of Rylsk had lost power after being damaged in an attack by Ukraine.
The reports come after Moscow claimed in April to have regained control of the entire region, nine months after a Ukrainian forces launched a surprise invasion. Kyiv insists it still has soldiers operating across the border.
Two transformers at the substation in Rylsk have been damaged, according to acting governor of the Kursk region, Alexander Khinshtein, in a post on the Telegram messaging app.
He added two teenagers had been injured by shrapnel from the blast.
Multiple Russian military bloggers also reported that Ukrainian forces had attempted to cross into the village, posting images - as yet unverified by the BBC - of vehicles breaking through tank traps on the border.
On Monday, Ukrainian forces fired missiles over the border and crossed minefields in special vehicles, according to the bloggers.
"The enemy blew up bridges with rockets at night and launched an attack with armoured groups in the morning," blogger RVvoenkor said according to Reuters news agency.
"The mine clearance vehicles began to make passages in the minefields, followed by armoured vehicles with troops. There is a heavy battle going on at the border."
In a statement on Monday, Ukraine said: "Nine months after the start of the Kursk operation, Ukraine's Defence Forces maintain a military presence on the territory of Russia's Kursk region."
While there has been no official response from Moscow, some military bloggers have also published maps showing opposing forces attempting to cross the border in two places towards Tyotkino - near where the drone command unit that was hit.
Meanwhile, in Sumy - around 12km across the border from Tyotkino in north-eastern Ukraine - local authorities urged people to evacuate from two settlements, Reuters reported.
Ukraine originally made its surprise incursion into Kursk in August 2024 to create a buffer zone and protect Sumy and surrounding areas, while also hoping to use it as a bargaining chip in future negotiations.
Additional reporting by Victoria Bourne.
