Ukrainian forces have been ordered to withdraw from the key battleground city of Severodonetsk after weeks of fierce street fighting in a move that will be seen by Russia as a significant victory.

Ukraine officials said there was very little left to defend in the bombed-out eastern city, where hundreds of civilians remain trapped in a chemical plant.

The order to withdraw on Friday came four months to the day since Russian President Vladimir Putin sent tens of thousands of troops over the border, unleashing a conflict that has killed thousands, uprooted millions and reduced whole cities to rubble.

Luhansk regional governor Serhiy Gaidai said troops in Severodonetsk had already received the order to move to new positions.

"Remaining in positions smashed to pieces over many months just for the sake of staying there does not make sense," Gaidai said on Ukrainian television.

The withdrawal from Severodonetsk would mark the biggest reversal for Ukraine since the loss of the southern port of Mariupol in May.

The latest Russian advances appeared to bring the Kremlin closer to taking full control of Luhansk, one of Moscow's stated war objectives, and set the stage for Sievierodonetsk's twin city of Lysychansk to become the next main focus of fighting.

Vitaly Kiselev, an official in the Interior Ministry of the separatist Luhansk People's Republic – recognised only by Moscow – told Russia's TASS news agency that it would take another week and a half to secure full control of Lysychansk.

Meanwhile, the general staff of Ukraine's armed forces said its troops had had some success in the southern Kherson region, forcing the Russians back from defensive positions near the village of Olhine. (Reuters)