Whether or not schools remain open for key workers' children during the Easter holidays remains "under consideration, the Department of Education has said.
Almost 600 schools stayed open on Monday and nearly 800 will be open by the end of the week, according to Education Minister Peter Weir.
The NASUWT, Northern Ireland's biggest teachers' union, said it was unaware of plans directing schools to remain open over the holidays.
It added it would not agree with teachers having to work.
Northern Ireland national officer Justin McCamphill said: "During the period of continued closures, some schools may seek to provide childcare to priority households outside of term time (e.g. during the Easter holidays).
"However, I have not been made aware of any plans by the Department of Education to direct schools to open.
"The NASUWT recognises that some staff may agree voluntarily to support such provision.
"It is important that where teachers volunteer in this way there is clarity on how staff will be appropriately remunerated and with regard to insurances and indemnification.
"The NASUWT does not agree that teachers may be compelled to work during holiday periods."
The Ulster Teachers' Union said it was engaging with the Department of Education on a daily basis.
Union general secretary Jacquie White added: "Anything which may impact on teachers and schools in the coming weeks will be fully explored and interrogated."
Earlier this week a home childcare initiative was announced to meet the needs of key workers in the NHS.
It is open to those providing clinical care to coronavirus patients, health and social care workers supporting life-threatening emergency work and critical primary and community care provision, all other health and social care workers and key public sector workers.