Michael Fitzmaurice said, "If a cull is to take place on the three mink farms in Ireland, then we must take the opportunity to eradicate the mink in the wild".
Meanwhile, minks in other countries have also tested positive for the coronavirus, including outbreaks on mink farms in the United States.
Mink farming became an industry in Ireland in the 1960s but has declined over the past decade in line with wider European steps to regulate, restrict and ultimately ban the practice in many EU member countries.
Since ordering the cull in early November, the Danish government has been forced to admit that it had no legal power to order healthy minks outside contaminated zones killed, and the agriculture minister resigned Wednesday.
The move has left the three farms "devastated and without a livelihood", a representative of Fur Europe said. Jensen repeated his earlier apologies, offering particular regret to the country's mink farmers. There is no evidence that the mutated version is more risky but the government moved quickly out of safety, though it lacked the legal basis to order the killing of healthy animals too.
The culling was ordered after a mutated version of the coronavirus was found in some farms and had infected people.
Two weeks after sounding the alarm about a mutated variant of the new coronavirus in minks that could threaten the effectiveness of a future vaccine, Denmark said on Thursday (Nov 19) the strain has likely been eradicated.
The cull comes amid concern that a mutation of the virus could affect the rollout and efficacy of a Covid-19 vaccine. While the political rivals have also sought the PM's resignation, Frederiksen defended his government's decision to eliminate the minks population.
The Department of Agriculture plans to cull three mink farms in Ireland on the advice of Chief Medical Officer Dr Tony Holohan. Farmers will be compensated for the initial cull but it's understood that the farms will not reopen afterwards.
Viruses such as the novel coronavirus that emerged in China late a year ago mutate constantly and new variants are not necessarily worse than the previous ones.
The Irish mink farms - some of which received government grants as recently as 2017 to support rural employment - earn €25 to €80 per pelt.