Three people were killed in the Ukrainian attacks in the Kursk border region, Kursk governor Alexander Khinshtein said.
"The enemy blew up bridges with rockets at night and launched an attack with armoured groups in the morning," Russian RVvoenkor war blogger said on Telegram.
"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."
The Ukrainian attack in Kursk was reported by multiple other Russian bloggers including "The archangel of special forces" and Russian state television war correspondent Alexander Sladkov.
Three people were killed by Ukrainian attacks in the Kursk border region, the local governor Alexander Khinshtein said on Monday.
Two women died when a Ukrainian drone hit a car carrying five people, the official wrote on Telegram.
One man and two other women suffered bruises and abrasions.
One man was killed in another attack on a car, according to Khinshtein.
Ukrainian officials have not commented on any advances but prosecutors said Russian shelling and guided bomb attacks during the day killed at least three people and injured others in border villages in the neighbouring Sumy region.
Russian war bloggers published maps showing Ukrainian forces trying to push over the border in two places towards Tyotkino.
The Ukrainian military said on Monday that its forces struck a Russian drone command unit near Tyotkino on Sunday.
Local authorities in the Sumy region also called on people to urgently leave two settlements - Bilopillya and Vorozhba - lying 9-12km across the border from Tyotkino.
Russia's top general said last month that Ukrainian troops had been ejected from the Kursk region, ending the biggest incursion into Russian territory since World War II, and that Russia was carving out a buffer zone in the region of Sumy.
The Ukrainian military says the operation in Kursk region is continuing.
The Czech Republic will expand training for Ukrainian pilots and maintain a program to deliver artillery ammunition to Ukraine, Prime Minister Petr Fiala said on Monday after hosting President Volodymyr Zelenskiy.
Zelenskiy was in Prague as part of stepped up efforts to rally European partners while the US administration pushes for a ceasefire in the more than three-year-old war.
In a news conference with Zelenskiy, Fiala said a well-armed Ukraine was the best security guarantee in Europe.
He said the Czech Republic would expand training of Ukrainian pilots, including for F-16 jets, without giving details.
While the Czech Republic does not own F-16s, it has supplied helicopter simulators to Ukraine.
Zelenskiy supported the efforts for a Ukrainian-Czech F-16 training school.
"We are ready to implement this project as soon as possible," he said.
Zelenskiy said on Sunday at the start of his Prague visit that a ceasefire with Russia was possible at any moment.
He has called on allies to apply greater pressure on Russia and has said he and US President Donald Trump have agreed that a 30-day ceasefire was the correct first step towards ending the war.
with DPA