Some 400 schools are closed on health and safety grounds
Taoiseach Enda Kenny says the withdrawal of supervision services by the Association of Secondary Teachers in Ireland (ASTI) "doesn't help" the current situation.
Some 200,000 secondary school students are not in school today because of the industrial action.
Talks between the union and Government officials ended without agreement last night, as the ASTI confirmed its members are withdrawing supervision and substitution duties.
Education Minister Richard Bruton said he was "very disappointed" the ASTI was effectively closing hundreds of schools indefinitely over a dispute which he said essentially relates to just one hour a week of extra duties.
He told Newstalk Breakfast earlier: "We are paying the substitution money to every other teacher expect the ASTI - and the reason we're not paying it to the ASTI is that they unilaterally withdraw from the contracted work that they're obliged to do which is the one hour per week.
"They decided that they would no longer work that, although that extra work applies to 280,000 public servants across the public service, they would step out of working it and decide that they weren't going to continue.
"That stepped outside of all of the agreements - so the benefits of collective agreements that were made with the Congress of Trade Unions don't apply to people who won't comply with their contractual commitments".
Speaking about education at the Irish Times Brexit summit in Dublin, the Taoiseach took aim at the unions.
"Our education system has to be fit for 21st century propose - providing our young people with a solid foundation on which to develop their future skills, their career prospects, their entrepreneurial talents.
"The unilateral decision of ASTI to withdraw from supervision and substitution doesn't help that case".
This dispute stems from ASTI's withdrawal from working the 'Croke Park Hours'.
The department says these are one hour per week, for the 33 weeks of the school year, which are now a core part of teachers' duties.
"All other public servants work these hours - in most cases several multiples of the one hour per week in the case of teachers", it adds.
The ASTI vice president, Ger Curtain, told Newstalk Breakfast earlier his members have been providing supervision and substitution for free for three years.