The Irish National Teachers Organisation's urging the Department to "reconsider" its plan to resume special education this week.
In-class learning was set to resume on Thursday as part of a phased reopening of schools.
However in a statement on Monday, the primary union said a public health webinar earlier in the day failed to adequately address teachers "grave safety concerns".
It said teachers are anxious whilst community infection levels remain very high and that Thursday's resumption should be delayed.
INTO President Mary Magner said,"we have heard the concerns of teachers in recent days and, while teachers across the country are keen to get back to the classroom, they are scared."
She said, "teachers are committed to supporting their vulnerable pupils but the safety of staff is vital."
General Secretary John Boyle was critical of the government's communication on the plan.
He said, "the failure of Minister Foley and Minister Madigan to engage in proper consultation in the last two weeks has been very damaging and it has hampered the planning for the safe reopening of schools."
Mr Boyle said while some progress on some "key concerns" had been made in recent days, he said "there is more work to be done to ensure the safety of staff, pupils and their families, including a higher prioritisation of education staff for vaccination".
The union said it will continue to engage with the department and public health authorities to work towards a "safe, phased reopening" but "up-to-date, reliable information and supports are essential" if this is to succeed.
The INTO's Central Executive Committee will meet again on Tuesday to assess the situation further.