Russia has announced that it is withdrawing forces in the eastern Kharkiv region of Ukraine, after Ukraine said its troops had made sweeping gains in the territory held for months by Russian forces.

"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 defence ministry said in a statement.

Ukrainian President Volodymyr Zelensky said tonight that Ukraine's armed forces have liberated around 2,000 square kilometres of territory since a counter-offensive against Russia started earlier this month.

In a video address, he also said that the Russian army was making "right choice" by fleeing.

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 minimise 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," Mr 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 neighbouring Lugansk region have been under the control of Moscow-backed rebel groups since 2014.

Ukrainian forces have recaptured dozens of towns and villages held by Russia for months, since bursting through the frontline earlier this week.

Early today, Ukrainian officials posted photos of their troops raising the country's blue and yellow flag in front of city hall in Kupiansk at dawn.

Ukrainian officials stopped short of confirming that they had recaptured Izium, but President Volodymyr Zelensky's chiefof staff posted a picture on social media of grapes.

The word "Izium" means "raisin" in Ukrainian and Russian.

Izium's sudden abandonment marked Russia's biggest battlefield defeat since its forces were forced to abandon their assault on the capital Kyiv in March.

Russian forces had fought hard to capture the city early in the war, and then used it as the logistics base for one of their main campaigns - a months-long assault from the north on the adjacent Donbas region.

Recent days saw Russian troops rapidly abandon dozens of towns and villages after their frontline collapsed in the face of the fastest organised Ukrainian advance of the war.

In Hrakove, one of dozens of recaptured villages, Reuters saw burnt-out vehicles bearing the "Z" symbol of Russia's invasion.

Ammunition boxes were scattered with strewn rubbish in positions the Russians had abandoned in evident haste.

"Hello everyone, we are from Russia," was spray painted on a wall. Three bodies lay in white body bags in a yard.

The regional chief of police, Volodymyr Tymoshenko, said Ukrainian police had moved in the previous day, and had checked the identities of local residents who had lived under Russian occupation since the invasion's second day.

"The first function is to provide help that they need. The next job is to document the crimes committed by Russian invader son the territories which they temporarily occupied."

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