The Minister for Education has warned teachers that any union that breaks partnership will have to suffer the consequences.
Speaking after two teachers' unions backed calls for industrial action at their conferences, Mary Hanafin said this was not the time to rock the boat.
She said unions did not have the right to break the Towards 2016 agreement.
The Minister said she thought it would be very, very wrong to even contemplate strike action.
The ASTI General Secretary, John White, has said the union was in favour of educational reform, but would not be co-operating with demands for what he called bureaucratic productivity.
Mr White told delegates at the union's annual conference in Killarney that bureaucratic burdens on schools involving endless paper trails served to distract teachers from their real work.
Later he said that if lack of progress on teachers' pay caused other unions to go on strike, the ASTI would not be found wanting in that regard.
Delegates attending the Teachers Union of Ireland annual conference in Wexford voted today to support a one-day strike in schools over lack of facilities for difficult students.
Members said they had made the decision in protest at what they believe was the failure of Ms Hanafin to provide proper support to deal with unruly students.
The union said that the wider membership would have to be balloted on any move towards industrial action.
