Russia on Friday said it captured several strategic heights near Kupiansk, an eastern Ukrainian city where Moscow's troops stepped up pressure in August.
Ukraine launched a counteroffensive against Russian positions in the south in June but Russia responded by trying to take back territory in the north east.
"In the direction of Kupiansk, units of the Western group of forces improved the tactical position by capturing enemy strongholds and key heights," the Russian defence ministry said.
It also claimed Ukrainian forces had sustained "significant" losses.
Kupiansk and territory nearby in the Kharkiv region were retaken by Kyiv last September, but Moscow is pushing back.
Ukrainian officials ordered vulnerable people to evacuate from several villages near Kupiansk, citing an uptick in Russian shelling.
The Russian defence ministry Friday acknowledged that fighting in the south and east of Ukraine was "difficult".
It said Ukrainian military command was staging "meat grinder" assaults without providing sufficient cover for their troops.