The three teacher unions have voted for an emergency motion backing industrial action, up to and including strike action, if they are not prioritised for vaccination.
The move follows last week's Government decision to roll out Covid-19 vaccinations based on age rather than profession.
The decision had angered teachers, who argue that they face significant risk of infection because of their exposure to students from multiple families in congregated settings where ventilation may be poor and social distancing poses a challenge.
The resolution says the changes "were announced by Government without consultation with workers' representatives".
It demands that the Government reinstates education staff as a priority group, considering what it states is "the essential nature of their work which requires them to be in daily contact with a large number of people from a large number of households" and secondly "that social distancing is problematic and not assured given the crowded nature, structure and layout of our workplaces".
The motion also demands early vaccination within the overall cohort of education staff, of pregnant teachers, those in higher risk categories and those who work in special schools, special classes, and home school community liaison teachers.
It states that "in the event that Government does not agree to schedule by the end of the current school year, vaccinations on the basis demanded above, Convention mandates a ballot of members for industrial action, up to and including strike action".
The Teachers' Union of Ireland, the Irish National Teachers' Organisation and the Association of Secondary Teachers in Ireland are holding their annual conferences online.
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Minister for Education Norma Foley told TUI members that she understands it is difficult for teachers to hear that they will not be prioritised for vaccination.
She said she met Deputy Chief Medical Officer Dr Ronan Glynn and they discussed that age was one of the strongest factors when it comes to vaccinations for Covid-19.
TUI General Secretary Michael Gillespie pointed to the United Nations and World Health Organization, both of whom say teachers should be prioritised for early vaccination.
"As we have stated at all times, it is only after the most vulnerable in society have been catered for that teachers should become part of a parallel programme that would recognise the significant health and safety issues around their key role as essential workers," he said.
He reiterated that the TUI had been given a commitment from the Department of Education on 10 and 23 February that teachers would be prioritised for vaccination as part of the first third of the adult population.
TUI President Martin Marjoram told the minister that his members "hate surprises" and they learned about the vaccination from leaks and distressed texts.
He said those with serious illness should be prioritised and would not put themselves before any groups.
Mr Majoram urged Minister Foley to reconsider vaccinating teachers, especially those working in special schools as they are usually younger teachers.
Earlier, Minister Foley said: "It has never been in the gift of the Department of Education ... to make a promise on vaccination priority ... the vaccination schedule was designed by the National Immunisation Advisory Committee and endorsed by public health."
Speaking on RTÉ's Morning Ireland, she said the decision to change the vaccination roll-out is a decision based on the science available now.
The education sector said it would accept the recommendation of public health every step of the way and has done so, she said, pointing out that new measures have been introduced as soon as they were recommended.
Ms Foley said NIAC's recommendation is "very, very clear" and all evidence points to the fact that people are most vulnerable, based on their age.
She said schools are proven to be areas of low transmission and this must be a key consideration.
Sinn Féin's education spokesperson Donnchadh Ó Laoghaire said teachers should be in a priority category, but he does not want to see them engage in industrial action.
Speaking on the same programme, he said it was wrong to change the roll-out without consultation.
He called on Ms Foley to engage with unions to avert the potential for industrial action.
ISME Chief Executive Neil McDonnell said the Government must not "buckle on this issue" as doing so would invite every interest group to come looking for earlier vaccination.
He said that ISME has "politely suggested that unions should not be going near this issue" and any decision by teachers on industrial action would have a huge impact on students.
Additional reporting by Ingrid Miley