There is still a “real risk” that many schools will only be able to open part-time, according to a union representing many principals.
The warning comes from the National Association of Head Teachers (NAHT) in a briefing paper to Stormont’s Education Committee.
Re-opening to all pupils full-time “will not be achievable in some or many schools,” the NAHT said.
The Education Committee is due to hear from teaching unions on Friday.
Meanwhile, a leading grammar school principal has called for action to avert “more mayhem” over A-level exams in 2021.
Education Minister Peter Weir said on Wednesday that opening schools was probably the “top priority” for the executive.
But the NAHT briefing to the committee, seen by BBC News NI, warns that there is a “substantial burden” on principals to ensure schools are safe.
According to Department of Education (DE) guidance school leaders, for example, must carry out individual risk assessments to assess whether it is safe for some vulnerable staff and pupils to return to school.
“School leaders have been left unsupported to make serious decisions on risk with potentially very serious ramifications,” the NAHT said.
“What immediate and ongoing assistance will be given to principals to ensure staff and pupils who are extremely clinically vulnerable are kept safe?
“The guidance states risk assessment should be undertaken but principals are not qualified to assess medical risk to individuals.”
The union also said a helpline for parents worried about sending their children back to school should be set up by the department.
The NAHT briefing warned that not all schools may be able to fully re-open but, if they do, they may need to return to a part-time timetable.
“Full restart will not be achievable in some or many schools and, in other cases, restart may begin for all children but then be forced to resort to a part-time model,” the document said.
“Schools will also need to plan for localised lockdowns.
“This may force some schools to operate on a part-time basis.”
The NAHT also called for additional guidance to be provided to special schools on re-opening.
Meanwhile, the principal of Wallace High School in Lisburn, Deborah O’Hare, has said that pupils going into Year 14 are in danger of becoming “lost students”.
In an open letter published on the school’s website, she said decisions needed to be made now about how their A-level courses would be assessed.
“We cannot be certain that some young people will not have their education further disrupted by Covid-19,” she wrote.
“How are the gaps in their educational experience going to be filled and how can government and awarding bodies ensure that the summer of 2021 is not marked by yet more mayhem?
“If the Covid-19 pandemic has shown us one thing it is the fragility of the examination system, a system which in many respects has seen little change over the decades.
“Perhaps in the ‘new normal’ we will move towards a system which will value the academic competence of teachers, acknowledge their insight and integrity and trust their genuine knowledge of students.”