BEIRUT — It’s too dangerous to bury east Aleppo’s dead in the daylight. So when night falls, an imam slips out to the latest mass grave, conducting the briskest of rites and thanking God that the skies have stayed silent.

With President Bashar al-Assad’s warplanes circling and ground troops closing in, Aleppo’s rebel-run districts are in such chaos this week that no one can count the dead.

“We can’t keep up,” said Ibrahim Abu Laith, a volunteer with the White Helmets civil defense group. “We’re having to choose who we find and who we don’t.”

Syria’s 5 ½-year war has proved so difficult to track that the United Nations said last year that it had stopped counting casualties at the half-million mark. Yet the scale and ferocity of the bombardment in east Aleppo since the start of a pro-government offensive on Nov. 15 has posed documentation challenges unseen in this war.

Last week, the opposition-run health directorate put the death toll at 508. Despite daily bombardment, there has been no update since.

While a local morgue records what details it can, the knock-on effects of a government siege mean many deaths go unrecorded. Casualties are treated across family basements and old fruit stores, and without enough gasoline to take bodies for autopsy, many people now opt to take them straight for burial.

Crippled by shortages, even the White Helmets choose their rescue missions carefully — wasting too much gas to reach one blast site could rob them of the chance to save more lives at another.

When they do venture out, the rumble of warplanes can swiftly abort an operation. This weekend, Laith said that he heard whimpers from the rubble as his team scrambled away.

“When you hear someone alive but reach them dead, that is the hardest part,” he said. Broken buildings across east Aleppo could still hide dozens of bodies, according to the local health directorate.

Some have been torn apart by follow-up airstrikes.

The head of Aleppo’s White Helmets branch watched last week as two women combed a body bag for signs of their loved ones. “Suddenly, the mother cried out and reached for a leg. She said he was her husband. She knew his jeans,” Ammar al-Selma said.

Then her companion recognized a watch. “All that was left of her son was his arm,” Selma said. “We’re bringing in body parts at this stage.”

The United Nations’ humanitarian chief warned Wednesday that east Aleppo is becoming “one giant graveyard.”

Already the cemeteries are full, local officials say, and shallow graves are spreading throughout public parks as families try to bury their dead quickly.

But even that is a gamble. As a government advance through northeast Aleppo sent tens of thousands of civilians fleeing Sunday, a young nurse, Modar Sheikho, narrowly escaped the artillery shell that killed his brother. His father’s death followed swiftly — hit by a bomb as he searched for a burial plot.

The only remaining option is the local council’s nighttime ritual, venturing out in a quiet moment to bury the day’s remains.

“You know, it is not our job to bury people. But if we don’t, no one else will,” said Abo Jaafar, an east Aleppo coroner.

“Where we used to bury one man, we lay down entire families now,” he said. “We dig and we dig. It never ends.”

Zakaria Zakaria in Istanbul contributed to this report.