Serhiy Gaidai said in a Telegram post that Russian troops had entered Sievierodonetsk, the biggest city held by Ukraine in the eastern Donbas region, where Russia's biggest advance for weeks has shifted the momentum of the three-month-old war.
Russia has been trying to trap Ukrainian forces in Sievierodonetsk, where Gaidai previously said 90 per cent of buildings were destroyed, and Lysychansk, its twin city across the river.
"The Russians will not be able to capture Luhansk region in the coming days as analysts have predicted," Gaidai said on Telegram, referring to the near-surrounded cities.
"We will have enough strength and resources to defend ourselves. However it is possible that in order not to be surrounded we will have to retreat."
He said fighting continued on Sievierodonetsk's outskirts but evacuations were still possible even though a key road out "is completely under fire".
Russia's separatist proxies said they now controlled Lyman, a railway hub.
Ukrainian officials said Russia had captured most of the town but said Ukrainian forces were blocking an advance to Sloviansk, a city a half-hour drive further southwest.
Ukrainian presidential adviser Oleskiy Arestovych said overnight that the well-organised attack on Lyman showed Russia's military, which was driven back from the capital Kyiv in March, was improving its tactics and operations.
A Ukrainian retreat could bring President Vladimir Putin closer to his stated goal of capturing the Donetsk and Luhansk regions of east Ukraine in full.
UK Prime Minister Boris Johnson told Bloomberg UK that Putin "at great cost to himself and to the Russian military, is continuing to chew through ground in Donbas".
Russian forces gained ground in the Donbas area after piercing Ukrainian lines last week in the city of Popasna, south of Sievierodonetsk.
Russian ground forces have now captured several villages northwest of Popasna, the UK's defence ministry said.
Reached by Reuters journalists in Russian-held territory on Thursday, Popasna was a burnt-out wasteland.
The bloated body of a dead man in combat uniform could be seen lying in a courtyard.
Natalia Kovalenko had left the cellar where she sheltered to live in the wreckage of her flat, its windows and balcony blasted away.
She said a shell hit the courtyard outside, killing two people and wounding eight.
"I just have to fix the window somehow. The wind is still bad," she said.
"We are tired of being so scared."
In the south, where Russia has seized a swathe of territory since the February 24 invasion, Ukrainian officials believe Russia aims to impose permanent rule.
Ukraine's military said Russia was shipping in military equipment from Crimea to build defences against any Ukrainian counter-attack and was mining the banks of a reservoir behind a dam on the Dnipro River that separates the forces.
In the Kherson region, north of Crimea, Russian forces were fortifying defences and shelling Ukraine-controlled areas on a daily basis, the region's Ukrainian governor Hennadiy Laguta told a media briefing.
He said the humanitarian situation was critical in some areas and people were finding it almost impossible to leave occupied territory, with the exception of a 200-car convoy that left on Wednesday.
On the diplomatic front, European Union officials said a deal might be reached by Sunday to ban deliveries of Russian oil by sea, accounting for about 75 per cent of the bloc's supply, but not by pipeline - a compromise to win over Hungary and unblock new sanctions.
