The union last month withdrew from the partnership system in the company, a key grouping which is designed to ensure harmonious industrial relations and oversees the implementation of the company cost-cutting programme.
The union is angry that the company has not implemented full union recognition at the mobile subsidiary. Eircom, which is 35% owned by an employee share ownership trust, acquired Meteor almost a year ago.
Under its previous owners, the American company Western Wireless, Meteor operated as a non-union company. However, the CWU successfully pursued a claim through the Labour Court claiming the right to represent 60 call centre workers at the company.
Meteor employs more than 600 staff.