Mariupol’s defenders on Monday held out against Russian demands that they surrender, the number of bodies in the rubble of the bombarded and encircled Ukrainian city remained shrouded in uncertainty, the full extent of the horror not yet known.

With communications crippled, movement restricted and many residents in hiding, the fate of those inside an art school flattened on Sunday and a theatre that was blown apart four days earlier was unclear.

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More than 1,300 people were believed to be sheltering in the theatre, and 400 were estimated to have been in the art school.

Perched on the Sea of Azov, Mariupol has been a key target that has been relentlessly pounded for more than three weeks and has seen some of the worst suffering of the war. The fall of the southern port city would help Russia establish a land bridge to Crimea, seized from Ukraine in 2014.

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But no clear picture emerged of how close its capture might be.

“Nobody can tell from the outside if it really is on the verge of being taken,” said Keir Giles, a Russia expert at the British think tank Chatham House.

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Over the weekend, Moscow had offered safe passage out of Mariupol — one corridor leading east to Russia, another going west to other parts of Ukraine — in return for the city’s surrender before daybreak Monday. Ukraine flatly rejected the offer well before the deadline.

Mariupol officials said on March 15 that at least 2,300 people had died in the siege, with some buried in mass graves. There has been no official estimate since then, but the number is feared to be far higher after six more days of bombardment.

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For those who remain, conditions have become brutal. The assault has cut off Mariupol’s electricity, water and food supplies and severed communication with the outside world, plunging residents into a fight for survival. Fresh commercial satellite images showed smoke rising from buildings newly hit by Russian artillery.

“What’s happening in Mariupol is a massive war crime,” European Union foreign policy chief Josep Borrell said.

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Mariupol had a pre-war population of about 430,000. Around a quarter were believed to have left in the opening days of the war, and tens of thousands escaped over the past week by way of a humanitarian corridor. Other attempts have been thwarted by the fighting.