Vets are consulting rhino specialists in Africa and North America, as well as virologists and other experts.
"So far, the investigation has ruled out exposure to toxins, bacterial infection, snake venom and organ failure as cause of death."
Staff are also investigating possible viral causes.
The remaining three white rhinos in the herd are being monitored.
Greens senator Lee Rhiannon said it was time for an independent inquiry into the Endangered Species Breeding Programmes at the Western Plains and Taronga zoo.
It's the second time the Greens have made such a call, after allegations that inadequate care led to the death in 2007 of Kua, a pregnant rhino destined for Western Plains Zoo for breeding.
"Captive breeding programmes are contentious, with animals exposed to a variety of health threats," Rhiannon said. "Captivity poses its own threats to the survival of animals not experienced in the wild."
She said a US research paper had concluded that black rhinos in captivity displayed unusual disease syndromes not described in the wild.
"Any captivity that does not replicate rhinos' natural habitat increases stress. It is well known that stress compromises the immune system," Senator Rhiannon said.
"With viruses most virulent before they cause death, there could well be other animals infected at the zoo."
Intombi and Aluka arrived the zoo from the Kruger Park in South Africa in 2003. Amira and Izizi were born in captivity. Amira, which means princess, was born at the zoo in 2005 and was hand-reared by staff. Their ages ranged from around seven to 16 years old.
The white rhino is usually grey. Its main difference from the black rhino is in the shape of the upper lip. White rhinos are almost endangered, with a wild population of about 14,500.
Rhiannon said the inquiry should also look at whether captive breeding programmes were the best way of preserving endangered species or whether public funding would be better spent on habitat protection.
- AAP