The GWU has declared an industrial dispute with the Ministry of Justice and Home Affairs, accusing it of foot-dragging in talks about correctional and immigration officers.
The union said the majority of the two groups of workers had become union members.
An initial introductory meeting had been held with the ministry, it said, but the ministry had since delayed holding more meetings to discuss an improvement of working conditions.
The union said it was not prepared to accept any more delays and is not excluding industrial action.