It was not immediately clear how much Ukraine had advanced in the region, but pro-Kremlin military bloggers reported earlier that a powerful new offensive was under way.
The assault comes at a critical juncture in the nearly three-year conflict, with both sides seeking to strengthen their negotiating hand ahead of US President-elect Donald Trump's return to the White House on January 20.
"At about 9:00 am Moscow time (0600 GMT), in order to halt the advance of Russian troops in the Kursk direction, the enemy launched a counterattack," the Russian defence ministry said.
The Ukrainian army did not comment on the operation, simply saying in its daily report that fighting was under way in the Kursk region without elaborating.
Ukraine used two tanks, a dozen armoured vehicles and a demolition unit in the assault, which was directed towards the village of Berdin -- about 15 kilometres (nine miles) northeast of Sudzha, Moscow said.
"The operation to destroy the Ukrainian army formations continues," it added.
Pro-Kremlin military bloggers acknowledged the Russian army had come under pressure but said Moscow was fighting back.
"The main events of the next attempted offensive by the Ukrainian army are clearly still ahead of us," influential pro-Russian Telegram channel Rybar said.
Images purportedly showing a column of Ukrainian armoured vehicles driving through the snow were shared by pro-Russia military blogger Dva Mayora on Telegram.
Ukrainian officials gave little detail on the new offensive, with a prominent lawmaker urging silence.
"I can't understand why it is necessary to officially report on the Kursk region. Maybe better to do it afterwards when the operation is over?" Ukrainian MP Oleksiy Goncharenko said.
Other officials expressed their glee at the operation, which comes almost three years since Moscow launched its full-scale military assault on Ukraine.
"Russia is getting what it deserves," Ukrainian presidential chief of staff Andriy Yermak said.
The head of Ukraine's Center for Countering Disinformation, Andriy Kovalenko, said on Telegram that defence forces were "working" in the area, without elaborating.
"In the Kursk region, the Russians are very worried because they were attacked from several directions, and it was a surprise for them," he said