Russian forces have withdrawn from key eastern towns, as a rapid Ukrainian counter-attack makes further gains.

Ukrainian officials said troops entered Kupiansk, a vital eastern supply hub for Russian forces, on Saturday.

Russia's defence ministry then said its troops have retreated from nearby Izyum to allow them "to regroup".

The ministry also confirmed the withdrawal of troops from a third key town, Balaklyia, in order to "bolster efforts" on the Donetsk front.

The Ukrainian advances - if held - would be the most significant since Russia withdrew from areas around Kyiv in April.

In his nightly video address on Saturday, President Volodymyr Zelensky claimed that Ukraine had now liberated 2,000 sq km (700 sq miles) from Russia since beginning a renewed counter-offensive earlier this month.

His claim would suggest that half of that area has been recaptured in the last 48 hours alone - as it is twice the area of territory Mr Zelensky said had been liberated when he spoke on Thursday evening.

Russia's admission of a withdrawal from Izyum is significant because it was a major military hub for Moscow.

"A three-day operation was carried out on the drawdown and organised transfer of the Izyum-Balakliya group of troops to the territory of the Donetsk People's Republic," the Russian statement said.

"In order to prevent damage to the Russian troops, a powerful fire defeat was inflicted on the enemy."

Shortly afterwards, the chief administrator of Russian-controlled parts of the Kharkiv region recommended that its residents evacuate to Russia "to save lives", according to the Russian state-run Tass news agency.

And the governor of the neighbouring Belgorod region, in Russia, said mobile catering, heating, and medical assistance would be available to people queuing to cross the border.

The advances will be seen as a sign that Ukraine's army has the capacity to retake Russian-occupied territory, crucial as Kyiv continues to ask its hard-pressed Western allies for military support.