The Department of Education, Sport and Culture (DESC) on the Isle of Man says that the safety of school children on the Isle of Man "can't be guaranteed".
This comes as teachers on the Island escalated their industrial action in a dispute over pay and working conditions.
Members of the National Association of Schoolmasters Union of Women Teachers (NASUWT) have stopped doing certain jobs asked of them due to the dispute.
Some of these jobs involve covering break time duties.
The Isle of Man Government has said that it may need to close schools to some year groups in response to the industrial action.
DESC met with NASUWT on Friday to discuss the ongoing trade dispute.
The Government department had been organising break time cover to "ensure students were safe", but "this is no longer sustainable and means some schools might be forced to close".
A statement says how the Department is "deeply disappointed that the NASUWT continue to escalate action - especially after teachers received an uplift between 2% - 7.6% and was backdated to 1 September 2021."
In April, NASUWT said that there has been a "failure of the Manx Government to improve pay and tackle excessive workload".
They say there has been a 30% pay freeze since 2010 for Manx teachers.
The Union's general secretary, Patrick Roach, has previously said that teachers are being "taken for granted".
DESC say that there will be more talks about pay scheduled for October.
These will involve all recognised teaching unions will happen once the School Teachers' Pay and Conditions Document (STPCD) has been ratified. DESC said how they are "unsure as to what the continued escalation at this point will achieve".
The Government Department also added how they are "concerned that without appropriate cover at break times, the safety of students will be put at risk".