The petition, launched by a vet and former vet from the Southern Isles Veterinary Practice on Benbecula, has been under consideration by the Scottish Government since April 12.
David Buckland and Graham Charlesworth are concerned the Soay Sheep on the archipelago's largest island of Hirta, are being left to starve and suffer, pushing for intervention to prevent this.
In the petition, Mr Buckland and Mr Charlesworth, said: "The St Kilda sheep have been feral since 1930, but millennia of domestication have altered their physiology, making them unsuited to life unmanaged.
"Information suggests overpopulation contributes to a yearly average of 600 sheep dying of starvation each winter on Hirta alone."
The National Trust for Scotland (NTS) and the Scottish Government cite their long-term adherence to the Animal Health and Welfare Act 2006 as the reason for the sheep's unprotected status.
The Act defines protected animals as those that are "commonly domesticated in the British Islands; under the control of a man on a permanent or temporary basis; or not living in a wild state."
A Scottish Government spokesperson said: “The population of sheep on St Kilda are considered to be an unowned and unmanaged population of wild animals much like other species such as wild deer.
"Their unique history also means they are not considered to be a species that is commonly domesticated within the British Islands.
“We recognise that within any wild population of animals in Scotland there will be different challenges from year to year which may impact population numbers. For the St Kilda sheep the harsher climatic conditions of the winter months can unfortunately lead to increased natural deaths among the population.”
The vets have called for the NTS to take steps to prevent the sheep from suffering, arguing there has been a lack of clarity around the Scottish Government's stance, with this causing confusion for the NTS, who help to manage St Kilda.
A NTS spokesperson said: “The NTS takes responsibilities relating to animal welfare seriously and always follows relevant legislation.
“The Soay sheep originate from the island of Soay where they were treated as a wild population for hundreds of years, unmanaged save for periodic hunting by the archipelago’s inhabitants.
“The sheep will continue to be treated as feral animals with a presumption against intervention, except in exceptional circumstances, such as a serious outbreak of disease that threatens the sheep populations.
“The trust has been in long-running communication with the petitioners regarding the management and welfare of the sheep on St Kilda. We will continue to comply with Scottish Government legislation relating to St Kilda’s sheep populations."
The sheep were introduced to Hirta by the Earl of Dumfries, but were then left as feral animals when his wool production plans failed four years after the last St Kilda residents left in 1930.
Since then their population has regularly fluctuated between 600 and 2,300 on the islands located around 40 miles north-west of North Uist.
The vets say they aim to enable "interventions to reduce the risk of winter starvation and the consequential suffering of the sheep".
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