Ukraine's President Volodymyr Zelensky on Friday said Ukrainian forces have recaptured nearly 2,500 square kilometres of territory from Russia in a counteroffensive that began late last month.

"This week alone, our soldiers liberated 776 square kilometres of territory in the east of our country and 29 settlements, including six in the Lugansk region," Zelensky said.

"In total, 2,434 square kilometres of our land and 96 settlements have already been liberated since the beginning of this offensive operation," he added in his daily speech shared on social media.

Ukraine has in recent days made a second significant push to reclaim territory in the northeastern region of Kharkiv, but also in the south, near Kherson, a city under Russian control.

In mid-September, Zelensky said Ukrainian forces retook 6,000 square kilometres from Russian troops in the first counteroffensive.

Russian forces said earlier on Friday they had captured ground in Donetsk in east Ukraine, their first claim of new gains since Kyiv grabbed the momentum with its lightning counteroffensive that rattled Russia's war effort.