Nicola Sturgeon said she was “angry” at footage filmed by animal rights charities, which showed the animals being killed on shooting estates.
She warned large-scale mass culls could put the conservation status of the species at risk and said legislation to protect the hares was among options being considered by government.
Landowners operate a voluntary restraint agreement regarding numbers culled.
Now gamekeepers shown in the footage have written to the First Minister and Environment Secretary Roseanna Cunningham to invite them to their estates to learn more about the rationale behind the killings.
Duncan MacKenzie, head gamekeeper for the Clune and Corrybrough Estates in Inverness-shire, said: “We’d really like to be able to show the First Minister around rather than discuss these issues in Edinburgh.
“I think it would be beneficial for everyone to get an understanding of why the hares need to be managed here.”
Mr MacKenzie said the estates were not hiding anything.