The enforcement notice orders Quinn to dismantle the factory and cease production.
Quinn has lodged the appeal believing that its planning application for the plant should be granted soon. If this application is approved, the enforcement notice will be unnecessary.
The council received the planning application in January 2008.
Quinn Glass director Peter Fitzgerald said: This is just the next step up in our fight to win the long-term security of our site in Elton. Quinn Glass plays an important role both within the community and the region we employ over 700 people from the area and boost the local economy with £4 million in taxes alone so securing the future of the plant is our utmost priority.
It is hoped the council will decide the fate of the factory in the next two months.
The appeal is the latest in a long-running legal battle between Quinn Glass and its direct competitor Ardagh Glass over the absence of planning permission for the Quinn glass plant. The enforcement notice was issued on 22 April (see MRW story).
The period to appeal the enforcement notice expired on 29 May.