The firm said the complaints lodged with the District Mining Bureau, Banská Bystrica had come as no surprise.
Chief executive Vassilios Carellas said: "We anticipated that complaints would be lodged against the decision of the District Mining Bureau, this therefore comes as no surprise.
"As always, we will continue to work closely with interested parties to address any, and all, concerns as they arise, which is all part of a normal, healthy and transparent engagement process."
Ortac told investors the matter had now been referred to the Slovak Central Mining Bureau for its decision, which is expected in the next month or so.
The permission to mine was granted by the District Mining Bureau subject to Ortac sticking to the plan it submitted, which specified ore extraction will be carried out using underground mining methods only.
Last month the firm was boosted after it unveiled drill results from the Yacob Dewar, Eritrean Copper-Gold project.
Ortac and partner, Andiamo Exploration, have begun a 1,400 metre drill programme on Yacob Dewar in Eritrea, and the latest drill results include 1.38% copper over 53 metres from the surface and 1.32% over 42.5 metres from surface.