The INTO has expressed concern over what it called the "disconnect" between the departments of Agriculture and Education over the recall of sanitisation products in schools.
INTO General Secretary John Boyle said the Department of Education has decided to recall the products, while the Department of Agriculture has said there is no need to discontinue using them.
Speaking on RTÉ's Today with Philip Boucher Hayes, Mr Boyle said the primary school system revolves around the principal teacher.
He said these teachers were looking forward to a break, but were now stuck with this, after some were already dealing with contact tracing and with the ViroPro hand sanitiser recall.
Yesterday, the Department of Education wrote to schools recalling more than 50 sanitising products, including hand sanitisers, wipes, detergents, and hand soaps.
It advised schools of "further safety concerns related to the items, which were all previously recommended for use on departmental procurement documents".
The recall comes after issues were found with the registration of the products during a review.
The principal of St Joseph's Primary School in Tipperary town said the anti-bacterial hand soap they were using in their bathrooms was recalled and it was left as problem for principals to sort, which she was able to.
Louise Tobin said it has been hectic at the school since March, and the mid-term break was a welcome reprieve up until yesterday's recall.
Another principal, Noirin Ní Mhaoldhomhnaigh, who is also a representative of the National Principals Forum, said this was "another whip at the back of school teachers" who were already tired.
She said she was able to secure a replacement order of sanitiser products and while this issue is serious, there are a long-ranging number of issues also not being addressed by the Government, which will have detrimental effects on school children for years to come if not rectified.
Mr Boyle also said the union has called for another review into the wearing of face masks in schools.
He said they are not calling for masks to be worn by children, but were simply asking health authorities to review the situation.
"It doesn't make sense to me for example that a child whose family have Covid-19 is not allowed to leave the house, except to go to school, so these are the inconsistencies that we really really need answers to," he said.
Speaking on the same programme, Sinn Féin's Education spokesperson Donnchadh Ó Laoghaire said the Department of Education is falling short of the mark in several ways on Covid-19 safety measures in schools and it "really needs to get a handle" on the issue.
He said the decision to recall sanitising products was right, but said he could understand how if tests and assessments were being carried out, how did so many slip through the cracks and have to be recalled.
He said the product recall is causing "huge disruption" for schools and has created an "absolutely chaotic" situation.
Mr Ó Laoghaire said if it does transpire that a school cannot open on Monday, because it has not been able to source alternative sanitisation products, it would be the department to blame rather than the school.
Earlier, Social Democrats Education spokesman Gary Gannon said Minister for Education Norma Foley should come before the Dáil to allay fears anyone may have following the latest recall of sanitisation products in schools.
Speaking on RTÉ's Morning Ireland, Mr Gannon questioned whether the Department of Education acted promptly in issuing the recall, as the products had been available since schools reopened.
He said there was a "serious breach or a fall down in protocol here and we need to understand why that happened".
Mr Gannon said the latest recall "impacts confidence and erodes morale" and leaves the school environment in a negative place again come Monday.
"Its absolutely important that we get it open, but that requires confidence, and it requires that school leaders, SNAs, teachers have a sense of confidence that the department has their backs, and what we've discovered over the last couple of months during the various different ineffective procedures that have happened is that doesn't seem to be the case.
"And this latest call that came through at 6pm yesterday that 52 sanitisation products are not suitable again impacts confidence and erodes morale."
He said he does support the reopening of schools, which he described as essential and we do not have the childcare capacity in Ireland to allow for another closure of schools.
He said during the lockdown a lot of children with special needs fell behind in their learning and that could not happen again.
Mr Gannon also said the issue will add to the ASTI's calls over school safety, adding that school morale is "on the floor" at the moment, with teachers and SNAs feeling "abandoned".
