Komala was a darling of one of India's oldest zoos.
Komala was found in agony last Friday
But the seven-year-old elephant calf died in agony after what officials at Msyore zoo in southern India are calling a conspiracy by insiders.
They suspect she could be the latest victim of poisoning by disgruntled employees, and, perhaps, a persistent campaign to discredit the zoo for reasons unknown.
Two elephants and an endangered lion-tailed macaque died in similar circumstances in August.
"This is shocking," the zoo's director, Manoj Kumar, told BBC News Online, as officials began an inquiry on Monday.
Karnataka state's Chief Minister, Dharam Singh, said he wanted a detailed investigation.
"The truth should come out. Officials have to be alert. There seems to be negligence."
The 110-year-old zoo in Mysore is home to 1,100 animals.
Komala, described as attractive and playful, was due to have flown to Armenia as a gift from Indian President APJ Abdul Kalam - she had been handpicked for her pleasing features, officials say.
Doctors battled for hours to save her on Friday, but in vain.
"It is really unfortunate. The elephant was to fly out on 14 October but we could not get a confirmed cargo booking," said Mr Kumar.
"The next date fixed was 30 October but destiny had other plans.
"We suspect foul play. All the deaths could be due to poisoning. We have taken the help of the police to catch the guilty."
He said Komala had died despite tight security arrangements following the deaths of the two other elephants, Ganesha and Roopa, and the lion-tailed macaque in August.
Zoo workers prepare for Komala's burial
The latter was a "breeder" on loan from a zoo in Madras as part of the lion-tail monkey conservation programme.
Zoo authorities called in the police after preliminary investigations revealed foul play.
Officials say Ganesha and Roopa had acute haemorrhagic enteritis and respiratory distress caused by zinc phosphide, normally used as poison for rodents.
This is not the first time animals have died mysteriously in captivity in Mysore, leading some to believe there is a plot to damage the state-run zoo's reputation - although it is not clear why anyone would want to do so.
An inquiry last year found foul play in injuries suffered by Meena, a popular chimpanzee.
Meena the chimp died after her arm was amputated
She died after an unsuccessful operation on her arm, which had been crushed by a sliding door.
Two emus from Australia also died in suspicious circumstances.
Closed circuit television is among the measures planned by the zoo authorities to monitor the movement of its feeding staff.
"Security is being revamped but I will not reveal the details," said Mr Kumar.