The group of 10 organisations, including the RSPB Scotland and the Scottish Wildlife Trust, say the animals are now being culled on a large scale across Scotland.
They want the practice to be banned until safeguards are put in place to allow sustainable management of the species, and ensure international conservation obligations are being met.
The Scottish Gamekeepers Association said the call for a ban was “environmentally irresponsible”.
Mountain hares - which are often found on grouse moors and are an important source of prey for golden eagles - are protected under the EU’s Habitats Directive.
The organisations say culling has developed relatively recently “in the belief that it protects red grouse against the tick-borne louping ill virus, despite the lack of scientific evidence to support this claim”.
Duncan Orr-Ewing from RSPB Scotland, said: “Mountain hares in their white winter coats are one of the most iconic species in Scotland. At present very little is known about their current numbers and population trends.
“We also don’t know what impact these large scale culls are having on mountain hares’ wider conservation status which could mean that the Scottish Government may be in breach of its legally binding international EU obligations to this species.”
In December 2014, Scottish Natural Heritage (SNH) announced the beginning of a three year study to trial methods of measuring mountain hare numbers.
As part of this, SNH called for a voluntary restraint of large scale culls on grouse moors.
Simon Jones from the Scottish Wildlife Trust said: “Mountain hares are important to Scotland both culturally and from a conservation perspective. We, along with the other organisations are calling for a three year ban, to allow time for all those involved to take stock of the longer term impacts of large scale culling.
“Once the results of the study have been published we will then be able to identify the best ways to monitor mountain hare populations and measure the impact that management is having on their conservation status.
“We believe that grouse moor managers have a duty of care to these important mountain hare populations. The unregulated and seemingly unsustainable culling that is endemic on many grouse moors is a threat to these important populations.”
A spokesman for the Scottish Gamekeepers’ Association said: “Allowing hare numbers to multiply uncontrolled over three years, as suggested, will have huge grazing impacts, including around forestry blocks, where culling currently takes place.
“The numbers of tick, already a growing problem in the countryside, will escalate, endangering any bird that nests on the ground, not to mention the potential repercussions for human health. It will be bad for birds and bad for biodiversity.
“The truth is that, away from managed grouse moors, mountain hare populations are at nothing higher than subsistence level yet groups asking for this measure have the power to change this today by introducing management regimes, on their own ground, to benefit hares. Why this is not done is the question which should be asked at the highest level.”
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