Ukraine's President Volodymyr Zelensky has ordered all civilians still living in parts of eastern Donetsk region under Ukrainian control to evacuate, reports BBC.
Speaking during a late-night address from Kyiv, Mr Zelensky warned of an intensification of fighting.
"The more people leave Donetsk region now, the fewer people the Russian army will have time to kill," he said.
The region has seen heavy clashes amid a slow advance by Russian forces, who already control large parts of it.
"The more people leave Donetsk region now, the fewer people the Russian army will have time to kill," the Ukrainian leader said. "We will use all available opportunities to save as many lives as possible and to limit Russian terror as much as possible."
Mr Zelensky's intervention comes as Russia invited UN and Red Cross officials to investigate the deaths of 50 Ukrainian prisoners of war (POWs) in another part of Donetsk region held by Russian-backed separatists.
The troops were killed in unclear circumstances during an attack on a prison in Olenivka, with both sides trading blame.
Speaking on Saturday evening, Russian defence officials said Moscow would welcome an "objective investigation" into the incident.
The Red Cross said on Friday it was asking for access to the Russian-run detention facility and to surviving prisoners - but no permission was immediately forthcoming.
Its deputy head of delegation in Ukraine, Daniel Bunnskog, said granting access to POWs was an obligation under the Geneva Conventions.
The Olenivka prison camp is controlled by the Russian-backed self-proclaimed Donetsk People's Republic (DNR).
What happened there on Friday remains unclear. Unverified Russian video footage of the aftermath shows a tangle of wrecked bunk beds and badly charred bodies.
On Saturday, Russia published a list of what it said were the 50 POWs killed in the strike. Moscow says the attack was carried out by Ukraine using a US-made HIMARS artillery system.
Kyiv denies carrying out the strike and has alleged that Russia fired on the facility to cover up evidence of war crimes.
Elsewhere, Ukrainian officials labelled Russia a "terrorist state" after Moscow's UK embassy tweeted that Ukrainian Azov battalion soldiers deserved a "humiliating death" by hanging.
Twitter acknowledged that the post from the Russian embassy violated the social media company's "rules about hateful conduct" - but added that it might be in the public interest to keep it accessible.
The tweet sent out on Friday night said that Azov "militants deserve execution, but death not by firing squad but by hanging, because they're not real soldiers. They deserve a humiliating death".
The tweet included a video clip showing a couple in a wrecked building, accusing Azov troops of having shelled their home. The embassy's call for execution repeats what the man in the video says.
Azov troops were forced to lay down weapons in May after fiercely defending for weeks Azovstal, a giant steelworks in the south-eastern port of Mariupol that was eventually captured by Russia.
The Azov Regiment is a nationalist group with far-right links when it was set up in 2014. It was later incorporated into Ukraine's National Guard.
Russia has long accused the regiment of being neo-Nazis and war criminals, as part of the Kremlin's propaganda campaign to justify its invasion of Ukraine on 24 February 2022.