A meeting between an ASTI group and members of the Joint Managerial Body in the row over teachers' supervision has adjourned and will resume again tomorrow.
The meeting at the Department of Education came a day after talks between ASTI and the Minister, Mr Dempsey, broke down after only an hour.
The dispute centres on a demand by ASTI that its members be paid for being on call for supervision duties. A deal brokered by the three teaching unions and the Department last year calls for teachers to be available for 37 hours of supervision per school year.
The Irish National Teachers' Organisation and the Teachers' Union of Ireland have agreed to the deal.
ASTI members voted by nearly three to two before Christmas to accept the deal, which would see them being paid €37 per hour for supervision.
However, ASTI is insisting its members be paid for being on call, whether they are required to supervise students or not. The union has offered to have its members available for 66 minutes per week - 37 hours over the course of the school term.
Mr Dempsey yesterday ruled out payments for being on call.
It is understood the Department and the Joint Managerial Body (JMB) is seeking a more flexible approach from teachers, whereby their hours can be carried over from week to week if they are not called to perform supervision duties.