Moscow announced Saturday that it was withdrawing forces in the eastern Kharkiv region of Ukraine, after Kyiv said its troops had made sweeping gains in the territory held for months by Russia's army.

"To achieve the goals of the special military operation to liberate Donbas, a decision was made to regroup Russian troops stationed in the Balakliya and Izyum regions, to bolster efforts along the Donetsk front," Russia's defense ministry said in a statement.

The apparent drawdown of Russian forces comes as Ukrainian troops said they had entered the town of Kupiansk in Kharkiv, with military observers saying Kyiv's army had advanced further still.

The defence ministry said that the withdrawal of troops from Kharkiv to the Donetsk region had been carried out over the course of a three-day operation designed to minimize Russian losses.

But in Donetsk, the Kremlin-backed leader of the separatist republic said there was fierce fighting between Russian forces and Ukraine.

Denis Pushilin said the situation in the town of Lyman in the Donetsk region was "very difficult" and that there was also fighting in "a number of other localities,", particularly in the northern part of the region.

"We have no other choice but to keep Donbas and we'll succeed. We'll win of course," Pushilin said.

Lyman, a former railway hub with a pre-war population of around 20,000 people, was captured by Russian forces in May.

Parts of Donetsk and the neighboring Lugansk region have been under the control of Moscow-backed rebel groups since 2014.