The Irish National Teachers’ Organisation has said the current public health advice will not allow all children to return to schools in September.
It said the two-metre social distancing rule is not physically possible in many classrooms.
The group said the Department of Education will publish a roadmap for the re-opening of schools in two weeks time.
It said teachers will have no difficulty returning to their full classes if the public health advice allows it.
It comes as secondary schools are implementing more rigid policies for remote learning from September.
A new policy document circulated by some secondary schools says they may provide students with internet access, desktop computers, digital imaging technologies and other devices.
It also says students are expected to follow the same rules for good behaviour and respectful conduct online as offline.
There are also guidelines for students to submit photos of work to ensure that it is legible.
John Boyle, general-secretary of the INTO, says the current two-metre social distancing guideline will be unworkable at many schools.
"We will probably have to have a number of plans in place: a plan for the full return of schools with all children and workers who are fit to go back at the one time, and then maybe a plan B or even a plan C - depending on the public health advice and that key issue of social distancing.
The Minister [Joe McHugh] was absolutely right when he stated that with the two-metre rules - he didn't say about us having the largest class sizes in Europe, but I suppose it's inherent in what he said - that it just wouldn't be physically possible to have all the children back together.
"But I would like to be optimistic about this that the country has been doing so well in suppressing the virus that we will get into a place in August where we would have certainty as to the number of children to go back".
It comes as Professor Luke O'Neill from Trinity College said the opening of schools should be done "cautiously".
He told Pat Kenny on Newstalk radio: "The evidence is even more compelling that children are not a major problem here, unlike flu.
"The schools closure is justified if it's a disease like flu because children pick that up among each other and then they go and spread it at home - that's why you close schools in a flu pandemic.
"This is a different virus with different properties - and the more it's gone on, the more we've realised this.
"Now there's really more and compelling evidence that kids aren't a big source of spread."
"But I can't see why a child can't go in for two days a week... and I think for the mental health of the children it's extremely important.
"And lots of studies have shown this in the past: that children kept outside of school will suffer academically later.
"And then the biggest reason of all is the vulnerable children who can't home-school - they benefit massively from being in school."
"There's no scientific evidence now to say that we shouldn't re-open schools cautiously".