The ASTI has called for talks with the Department of Education following the rejection by its members of measures to support implementation of the Senior Cycle redevelopment programme from this September.
Commenting on the comprehensive rejection by teachers' union members of the proposals, the union's General Secretary Kieran Christie said "we think there is scope for further engagement".
Asked about the possibility of additional talks now, Minister for Education Helen McEntee said Leaving Certificate reform will still go ahead this September and the package of measures that have been agreed will remain.
The ASTI rejection, and its strength, has come as a surprise to many as 67% of members rejected the plans in a ballot that had a high turnout - 73% of members.
Members also gave their union a mandate for action up to and including industrial action.
A week earlier, Teachers' Union of Ireland members voted to accept the measures.
The TUI leadership had recommended acceptance, whereas the ASTI made no recommendation to its members.
The ASTI rejection is a significant indication of the concern felt by teachers around aspects of the reform.
What it will mean for the implementation of Senior Cycle reform is not as yet clear. The union's next steps have yet to be agreed upon.
Its executive is due to meet in ten days' time and, according to Mr Christie, will "be looking at the outcome of the ballot and considering a way forward".
Mr Christie said there was "a need now for calm heads to prevail".
Teacher concerns centre on Additional Assessment Components which will be worth 40% of all marks in a revamped senior cycle.
The AACs will typically involve practical project work completed during the year which will then be written up into a report. This written report will form the basis for assessment.
Other concerns include the potential for students to use AI to cheat when writing these reports. There are also other concerns around equity.
The science subjects are among the first to be revamped, starting this September for students entering 5th year.
Biology teacher and member of the union's Executive Council Adrieanne Healy said teachers were looking for the changes to be paused for a year.
Calling the introduction "rushed", she said while some private fee-charging schools had state-of-the-art science laboratories as well as lab technicians, many other schools had facilities of a far lower standard.
She said teachers were concerned about the impact of this inequality on student outcomes.
Commenting on teacher worries around the potential misuse of AI by students, in order to cheat, Ms Healy said teachers could not understand why a system with "100% integrity" was being replaced with one with only "60% integrity".
The Minister for Education said reform of the Leaving Certificate will be an "absolute game changer" for students.
"This is about equipping our young people for what is an ever-changing world. It’s about taking our pressure off them, that absolute focus on exams at the end of the year and making sure we are testing their abilities, different skills, different requirements for people to move into the workforce," Helen McEntee said.
She said she acknowledged the ASTI statement but added "Leaving Cert reform will still go ahead this September".
"All of the unions have signed up to this as part of the public sector pay agreement," she added.