The Education Minister Richard Bruton says he cannot see any reason for secondary teachers to go on strike.
Their union the ASTI has warned they may take industrial action in their row over pay and claim it is unfair to pay recently hired staff less for the same work.
Members are currently voting on whether they will withdraw from supervision and substitution.
However, Minister for Education Richard Bruton says they are the very issues other teachers unions are covering in talks.
Mr Bruton said: "I certainly hope not, because I can't see the rationale for this dispute, and we have had very active discussions with both the TUI and the INTO - who are inside Lansdowne Road - on the very issues that the ASTI are now talking about industrial action."
Minister Bruton says the union made a decision to withdraw from the Lansdowne Road Agreement, and will therefore not get the benefits of it.
"There is the opportunity for the ASTI to sit down, along with the INTO and TUI, to make progress on this issue - but they have decided unilaterally that they don't want to do that.
"They've withdrawn the one hour a week and that puts them outside of Lansdowne Road, and puts them outside the chance to participate in these productive talks.
"In May this year the ASTI balloted and then directed their members to withdraw from these hours, so they have made a decision to withdraw from the operation of these hours and from the Lansdowne Road Agreement - and naturally they don't get the benefits of an agreement from which they have withdrawn and ceased to cooperate with," he told Newstalk Breakfast.