The General Secretary of the Irish National Teachers' Association has written to the Minister for Education calling for a delay to the start of the next school term until Monday, 11 January, "at the earliest".
Primary schools are due to resume classes on 6 January following the Christmas break.
In his letter, John Boyle said the number of confirmed cases had "grown at an alarming rate in the last fortnight with nearly 700 children of primary school age testing positive in the fourteen days prior to schools closing for the Christmas holidays".
He urged Minister Norma Foley and the Government to consider delaying the start of the next school term as they consider further Level 5 restrictions at today’s Cabinet meeting.
"In our view your government would also be better placed late next week to take account of emerging scientific evidence regarding the new variants of Covid-19 than you possibly could be within the next seven days," Mr Boyle said.
Earlier, the Minister for Health Stephen Donnelly said the Cabinet's position on schools "has not changed at all", adding that schools are still due to reopen, and that the public health advice on their reopening has not changed at all.
He said the Cabinet will look "right across the spectrum" and at the advice from the National Public Health Emergency Team (NPHET), which is seeking what he said was a "full Level 5".
The Cabinet will assess what the appropriate response is given the rising number of cases, Mr Donnelly added.
He said both the Government and NPHET were "very concerned" about several virus indicators, namely the rapid growth in cases, and the rising number of hospitalisations.
Asked what further measures could be imposed, based on where we are now versus "full Level 5", Mr Donnelly mentioned restrictions around retail, gyms, leisure centres, and home visits.
"Regardless of what measures we're at, the very, very clear message from Government and the public health doctors is we need to reduce our social contacts.
"We're seeing some people who've tested positive have up to 30 close contacts, which is far far too high. We're seeing social events where people clearly are not following the measures.
"Far too many people are coming to them and they're turning into these so-called super-spreader events," Mr Donnelly added.
He said just a week ago, there were 234 patients in hospital, but now there were 409 - a 75% increase.
The minister said Cabinet was very aware that Ireland has already moved to an amended Level 5 in terms of restrictions. Pressed further on what might change, he said he could not pre-empt any decisions ahead of the Cabinet meeting.
Mr Donnelly said there are two things being done at the moment - suppressing the virus, and rolling out the vaccine - adding that once the most vulnerable people are covered, then the risk profile for case numbers "changes dramatically".
A 'wonderful moment of hope'
On the vaccine rollout, he said today was a "wonderful moment of hope" in the country's fight against the virus, saying it marked the "beginning of a new chapter".
He said he was not sure on the exact numbers that would be vaccinated this week, but that the four sites where the vaccine is being rolled out today each received 500 doses to begin with, and that the process would be ramped up.
He said they were closely following the advice of the National Immunisation Advisory Committee (NIAC), to ensure that the rollout was done safely, and effectively, adding that they were cognisant of issues that have faced other countries.
Mr Donnelly said "nobody is sure" in terms of supply of the vaccine, adding that the plan will be determined based on how many doses they receive.
As of today they have 40,000 doses, and so the plan is to have 20,000 people vaccinated by mid-January. If additional doses come in as scheduled, it is hoped to ramp up to 40,000 a week, he explained.
Mr Donnelly said they hoped to avoid a situation whereby people receive their first dose, but then three weeks later they are not in a position to receive the second dose.
The plan is that by the end of February, residents and staff in nursing homes would be fully vaccinated, as well as thousands of other healthcare workers, the minister added.
'Full Level 5 will have to be considered'
A return to full Level 5 restrictions will have to be considered by Cabinet, a senior minister has said
Minister for Higher Education, Simon Harris, said the country is "in a time of great darkness in relation to Covid" and we are now in "a bad and worrying place".
Asked if this would lead to a return to full Level 5 restrictions, which would include the closure of leisure outlets and non-essential shops, Mr Harris said: "Certainly they will have to be considered, the Cabinet is not having its second meeting in three days to share Christmas greetings."
Meanwhile, the Minister for Housing Darragh O'Brien has said any measures taken to stem the rising Covid-19 case numbers will hopefully be for a much shorter term, given that the vaccine is now being rolled out.
Speaking on RTÉ's Drivetime, he said: "Any measures that we need to take, we will take," adding that decisions on closing down sectors to protect people are not taken lightly.
Mr O'Brien said the closure of non-essential retail and a further limit on domestic travel "were the only items remaining" that may be considered.