More than 3400 of the original 57,000 sheep abroad the vessel have already died during the five weeks the ship was stuck in the Middle East, said Hugh Worth, head of the Australian branch of the Royal Society for the Prevention of Cruelty to Animals (RSPCA) on Friday.
The herd is facing temperatures of 45-50C (113-122F) and many had died over the past few days, said Worth.
“The number of sheep dying is rapidly increasing because now they’ve been idle in the water for over five weeks,” Worth told National Radio.
“It’s a fairly hefty option to kill 57,000 sheep, less the 3500 that have already died but the fact of life is, what alternative have we got?” he asked.
The sheep were rejected last month by Saudi Arabia after a Saudi vet claimed 6% of the animals had the disease scabby mouth.
Australia rejected the claim, saying its own veterinarian abroad the ship found less than 0.5% of the sheep infected, and suspended all livestock shipments to Saudi Arabia in response to the incident.
A second, unnamed Middle Eastern country this week also refused to allow the sheep to be unloaded.
That prompted a spokesman from the opposition Australian Democrats party to demand the government order the sheep returned to Canberra abroad what he described a “ship of death”.
“They were very confident last Wednesday that they were going to disembark the sheep at a second port and that was untrue,” he said.
Officials have said the sheep are owned by a Saudi importer and it is his responsibility to find a new buyer.