Its goal is to penetrate deeper into the Donetsk region and envelope the pocket around the embattled city of Severodonetsk from the north, it said on Twitter.
If Ukrainian civilians do not take up an offer of leaving via a corridor, Russia is likely to claim justification in making less of a distinction between them and any Ukrainian military targets in the area, the ministry added.
Hundreds of people are ensnared in makeshift bomb shelters in the key city of Severodonetsk, which is in the Luhansk region, including at the besieged Azot chemical plant, governor Serhiy Gaidai said.
"It is now impossible and physically dangerous to get out of the plant due to constant shelling and fighting. There are 568 people in the shelter, including 38 children," he said.
Gaidai said this week that around 10,000 civilians remained in the city, which is controlled mostly by Russian forces.
The Ukranian army said on Saturday there was continuous "fire from artillery and rocket-propelled grenade launchers at the positions of our troops and civilian infrastructure".
Russian forces also launched missile strikes on Ukraine's largest oil refinery on Saturday, according to the regional governor in the central Poltava region.
"Kremenchuk (oil refinery) is again under enemy strike. Between 6 and 8 Russian missiles hit refineries and other infrastructure," Dmytro Lunin said in a Telegram message.
In the city of Lysychansk, also in Donbas and the target of Russian shelling, residents were preparing to be evacuated.
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Source: Reuters, AFP