The Department of Education has given the Association of Secondary Teachers in Ireland an ultimatum that if its members do not agree to co-operate with the Lansdowne Road Agreement by 30 June, they face serious consequences including potential compulsory redundancy.
However, Minister for Education Richard Bruton has also extended a further invitation to the union to take part in talks aimed at resolving the dispute.
The ASTI has rejected the LRA, which comes into force on 1 July when the Haddington Road Agreement expires.
Members have also voted to cease working 33 additional hours imposed under the Croke Park and Haddington Road deals - a move that could trigger school closures in the new academic year.
Under financial emergency (FEMPI) legislation, unions that repudiate the public service collective agreement (the LRA) can face significant penalties.
In the first of today's letters to the union, the Department warned that if the ASTI does not formally confirm by next Thursday that members will cooperate with the LRA - including working the additional hours - it will be taken that ASTI members will cease cooperating with the Agreement with effect from 1 July.
It said that in that event, the Department's intention is effectively to formally invoke the required procedures to apply the FEMPI measures to ASTI members from 1 July.
Those measures include non-restoration of pay cuts, certain pay cuts, an increment freeze, non-payment of supervision and substitution payments worth €1,600 a year and the loss of protection from compulsory redundancy.
Teachers made redundant would only receive the minimum statutory redundancy and newer recruits would lose more rapid access to a permanent contract.
The letter warned that if ASTI continues its refusal to cooperate with the LRA in the medium term, further measures may be considered.
However, in a separate letter, Education Minister Richard Bruton extended an invitation to further talks, outlining amendments to how the disputed hours could be worked.
An ASTI spokesperson confirmed that the union had received correspondence which will be considered on Monday and Tuesday when the union leadership meets in Limerick.
The Minister's letter said he is aware of teachers' concerns regarding the Croke Park hours and is willing to provide flexibility in how they are used to those cooperating with the LRA.
He said that as a first step, the maximum time available for planning and development work on "other than a whole-school basis" is being increased from five to eight hours from the beginning of the 2016/2017 school year.
He noted that it will increase to 10 hours from the beginning of the 2017/2018 school year.
He said that a review of the hours, due to get under way shortly, will have regard to teachers' professional judgment, system and school requirements and experience to date of best practice in the utilisation of the hours.
He said the review would also draw on existing good practice in making recommendations to optimise the most professional and valuable usage of the additional hours by teachers.
The Teachers Union of Ireland, which also represents secondary teachers and rejected the LRA, has agreed a deal to avoid imposition of the FEMPI penalties.