Parents reacted angrily to the weekend decision by the ASTI not to re-enter talks with the Government appointed mediator, Mr Tom Pomphrett.
The National Parents Council (post primary) said all 16,000 ASTI members should be balloted on re-entering talks.
Its president, Mr John Whyte, said members of the ASTI's central executive council "ignored the advice" of the union's leadership to accept the proposal.
He said teachers "on the ground" might have different views to the 180-member CEC.
He said parents who supported the teachers so far might change their stance because students were entering an exam period.
Mr Whyte said the only way the dispute would be solved was when teachers and the Department of Education discussed the pay issue in a "rational" manner.
However, Mr Whyte said his organisation wanted to dissociate itself from a plan by another parents' group to sue the Department of Education for its failure to ensure classes for pupils during the strike.
The action is being taken by parents from the Congress of Catholic Secondary School Parent Associations, which is a constituent body of the National Parents Council (post primary).
Their spokeswoman, Ms Barbara Johnston, said solicitors had advised them they had a strong case. She said a regional meeting would take place soon and parents would be asked to become part of the class action.
She said the case would draw on the constitutional provision that all citizens have a right to an education. She said the case would concern the six days when teachers were on work-to-rule and school managers refused to hold classes because of health and safety concerns.
On the ASTI decision, she said: "Parents will find it hard to believe that the issue of three days' pay can be allowed to hold up everything. The vote by ASTI seems unreasonable, some teachers are not behaving like adults. I think they need to act in more mature fashion." While parents were united in their condemnation of the ASTI action, this Saturday a meeting takes place which is likely to see their representatives clashing.
A major split emerged between a group led by Ms Johnston and a group led by Mr Whyte and Mr Sean Grehan, company secretary for the National Parents Council (post primary)
A meeting in Dublin is expected to hear claims that the National Parents Council (post primary) has not been strong enough in condemning the ASTI action.