Minister for Education Richard Bruton has said that he is seeking a meeting with the Association of Secondary Teachers Ireland next week.
On Friday, the union announced seven days of strike action in its dispute over pay for newly-qualified teachers and payment for supervision and substitution duties.
The work stoppages are scheduled to take place between now and December, resulting in the closure of secondary schools.
ASTI members will strike on 27 October, 8 November, 16 November, 24 November, 29 November, 6 December and 7 December.
Teachers will also withdraw from supervision and substitution duties from 7 November.
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The Opposition has said negotiation and a rebuilding of trust with public sector workers is the only way industrial action by teachers and others can be avoided.
Sinn Féin has said that the threat of docking teachers' pay is unhelpful.
Speaking on RTÉ's This Week, Mr Bruton said that a substantial deal was on the table to help address the issue of pay for newly-qualified teachers.
He said that any agreement with the ASTI would have to be within the terms of the Lansdowne Road Agreement.
The minister also said that it would be "very difficult" to keep schools open when the non co-operation with supervision and substitution duties begins as the ASTI has refused to co-operate with any contingency plan to cover these duties.