Civilians continue to seek refuge at a besieged steel complex in Mariupol.

Despite dire conditions at the Azovstal steel plant, the Ukrainian military’s last foothold in the key port city of Mariupol, civilians continue to arrive seeking shelter from Russia’s offensive, according to fighters there.

Maj. Serhiy Volyna, the acting commander of a Ukrainian Marine unit defending the plant, told The New York Times in a telephone interview on Friday that there were few places left in the city for residents to flee.

“There are various shelters that were used by civilians which have been destroyed,” he said. “These people come to us.”

Russia views capturing Mariupol as crucial to its aim of securing a land bridge along Ukraine’s south to connect Crimea to the Donbas, and its forces have been shelling the plant relentlessly. The plant has become the last refuge for thousands of trapped Ukrainian fighters and civilians. Efforts to establish safe evacuation corridors have been repeatedly foiled by Russia’s continued shelling, and there is little food left inside.

Over the past few days, Ukrainian forces at the steel complex have posted videos on social media calling attention to the dire situation there for civilians taking refuge, particularly women and children.

That civilians are still seeking to shelter there — with no prospect of escape or rescue — offers a testament to what they must be facing elsewhere in the devastated city.

“The amount of people changes and increases day to day,” Major Volyna said. “We have far exceeded what defines a humanitarian catastrophe.”