The fate of the city is hanging on an unknown number of defenders making their last stand at an iron and steel plant.
In addition to pounding the holdout in Mariupol, Russian forces have intensified their attacks elsewhere in the Donbas, home to coal mines, metal plants and factories vital to Ukraine’s economy.
Major Serhiy Volyna, commander of Ukraine’s 36th Separate Marine Brigade, appealed for help from world leaders in a dramatic video released on Wednesday.
“I have a statement to the world,” he said.
“It may be my last statement, because we have only a few days, or even hours, left.
“The enemy’s units are 10 times larger than ours.
“They have supremacy in the air, artillery, and units that are dislocated on the ground, equipment, and tanks.”
The Ukrainian commander estimated that there were “hundreds of civilians” sheltering on the territory of the plant, along with 500 wounded military personnel struggling for medical care.
“We appeal to world leaders to apply the extraction procedure to the military of the Mariupol garrison, to the civilians who are with us here at the plant,” he said.
“We ask you to take us to the territory of a third country and provide us with security.”
A few thousand Ukrainian troops, by the Russians’ estimate, remained holed up in the steel plant.
The Russian side issued a new ultimatum to the defenders to surrender Wednesday, but the Ukrainians have ignored demands to leave the plant’s labyrinth of tunnels and bunkers.
Even amid the Russian onslaught, there were renewed hopes on Wednesday of an evacuation of thousands of civilians from the shattered port city.
Mariupol Mayor Vadym Boychenko has urged locals to leave the city, though previous such agreements have fallen apart, with Russians preventing buses meant to pick up evacuees from entering the city or shelling escape routes.
“Do not be frightened and evacuate to Zaporizhzhia, where you can receive all the help you need — food, medicine, essentials — and the main thing is that you will be in safety,” he wrote in a statement issued by the city council.
Officials have given varying estimates of how many people remain in the city, which had a pre-war population of more than 400,000.
Cr Boychenko said about half had fled and asked those who had to contact relatives still in the city and urge them to evacuate, saying buses would be provided and one pickup point would be near the Azovstal steel mill.
Mariupol’s fall would deprive Ukraine of a vital port, complete a land bridge between Russia and the Crimean Peninsula, which Moscow seized from Ukraine in 2014, and free up Russian troops to move elsewhere in the Donbas.
If successful, Russia’s offensive in the Donbas would carve Ukraine in two and give President Vladimir Putin a badly needed victory following the failed attempt by Moscow’s forces to storm the capital, Kyiv, and stronger-than-expected resistance in the nearly two-month war.
But analysts say it could also devolve into a grim war of attrition as Russia attempts to defeat Ukraine’s most experienced, battle-hardened troops who already have been fighting pro-Moscow separatist forces for eight years in the mostly Russian-speaking Donbas.
With that potentially pivotal offensive underway, Russia said Wednesday it had presented Ukraine with a draft document outlining its demands as part of talks aimed at ending the conflict — days after Mr Putin said the negotiations were at a “dead end”.
“The ball is in (the Ukrainians’) court, we’re waiting for a response,” Kremlin spokesman Dmitry Peskov told a conference call with reporters.
He gave no details on the draft, and it was not clear when the Russian document was sent or if it offered anything new to the Ukrainians, who presented their own demands last month.
A Ukrainian presidential adviser said Kyiv was reviewing the proposals.