Frederiksen has insisted the cull is "non-negotiable", and her government is now preparing legislation to make it possible - by banning mink farming until January 1, 2022.
But the Swedish mink likely aren't infected by the same mutated strain, according to Danish authorities who said Thursday that the strain was now "most likely" extinct.
An agriculture ministry spokesman said that testing of Ireland's mink herd had yielded no positive Covid-19 tests to date.
They wrote, "We do not wish to spread alarm; however, we are deeply concerned that these facilities could, knowingly or unknowingly, be contributing to the spread of COVID-19 in the state, or could even house or come to house new mutations of COVID-19, like the one discovered in Denmark".
Outbreaks where the virus appears to have spread from animals to humans have been detected in six European Union countries.
There are around 100,000 minks in three farms across the country in Laois, Donegal and Kerry.
All farmed minks in Denmark have been culled because of coronavirus outbreaks among the animals and the discovery of the mutated strain, which authorities said showed reduced sensitivity to antibodies, causing fears it could compromise vaccines. Researchers from London used this information and managed to confirm cases of people infected by the mink-related COVID19 mutations in Denmark, UCL Genetics Institute director Francois Balloux said.
Following the announcement today, mink farmers accused the Government of culling healthy animals "without providing any scientific or legal basis".
The farms say all their workers and animals tested negative for Covid-19 last week and they have increased bio-security measures in recent months. Or chickens? Mink can easily be culled, they are non-essential.
But the country's department of health "indicated that the continued farming of mink represents an ongoing risk of additional mink-adapted (coronavirus) variants emerging", he said in a statement.
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