The area is about 10km from the Ukrainian border.
Russia said Ukraine had deployed two mechanised battalions, tanks and armoured vehicles in the attempted attack.
There has been no comment on the fresh offensive from officials in Kyiv.
But Zelenskyy on Thursday praised his troops fighting in the Kursk region and issued several units with state awards.
“The occupier can and should be beaten on its territory,” he said in a social media post.
“The Kursk operation clearly explains the meaning of the principle of ‘peace through strength’,” he said, referring to a message he has been promoting to secure ongoing military support from Ukraine’s western partners.
