The Department of Education, meanwhile, has also moved to allay fears of any shutdown.
The department said there are “no plans” for such a move, which would require “medical and scientific advice”.
The call was made by the NASUWT official Justin McCamphill yesterday, amid concerns about staff shortages.
Mr McCamphill, speaking to BBC Radio Ulster, said schools should close early for a “circuit-breaker”.
He also said the situation with staff shortages was “spiralling”.
“That is what we are hearing is happening all across schools in Northern Ireland and we expect over the coming weeks that situation is going to get worse,” he said.
“I think you will see that practice spreading to all schools, where schools are going to have to ration the resources.”
The DUP’s Sammy Wilson, a former teacher, described the suggestion that schools should be closed as “mad and daft”.
He questioned how Mr McCamphill had come to believe schools should close.
“Does Mr McCamphill recognise that there’s been enough damage done to children’s education over the last year-and-a-half?
“Leaving aside the need for parents to get to work and everything else, it’s been well documented now – the impact on children’s education, on children’s socialisation, on children’s mental health of these continual closures.
“There’s absolutely no justification, none whatsoever, other than the fact that some teachers – not all teachers – will use every excuse to get out of school.
“There’s no massive upsurge in cases [linked to schools]. There’s no damage being done to children’s health.
“We have no evidence of that at all.
“It is also true that it is far harder to teach children via Zoom, and by the computer and everything else.
“It is much easier to spot the child who might be struggling when you are actually in the classroom and offer help, or the child who is showing promise.
“This is just mad and daft.”
Asked if his party, which holds the education ministry through Michelle McIlveen, would oppose possible closures, Mr Wilson said: “Yes, absolutely – 100%.”
The department, meanwhile, stressed that while it would not be a decision for the education minister to make alone there are no “no plans” for an early shutdown.
A Department of Education spokesperson said: “There are no plans to close schools early for the Christmas period. Any decision to do so would be taken by the Executive and would be based on medical and scientific advice.”
The spokesperson continued: “Departmental guidance requires schools to continue to implement a range of mitigations to reduce the risk of Covid-19 transmission including: cleaning, ventilation, face coverings, consistent groups and regular asymptomatic testing using lateral flow devices for all staff and post-primary pupils. Vaccination is available to all staff and some students.
“Anyone displaying any of the key Covid-19 symptoms must not attend school. They should stay at home and book a Covid-19 test.”
The spokesperson added: “The PHA continues to provide, as required, specialist public health advice to schools on the management of multiple cases and clusters.
“However we must all be aware that Covid-19 is still active in our communities. It has not gone away and parents, pupils and indeed wider society need to stay vigilant and not become complacent. Everyone has a role to play in ensuring that hygiene, social distancing and all other public health measures continue to be followed.”
Earlier, a spokesperson for the department had told the BBC it is “aware of the ongoing difficulties faced by some schools in securing appropriate cover as a result of staff absence, and acknowledges that individual schools may need to consider a short period of remote learning for a class or classes, in response to local circumstances”.
The latest figures from the Department of Health, meanwhile, show that another two coronavirus deaths have been recorded.
There were also 1,585 new cases recorded in the most recent 24-hour reporting period.