PRIMARY school principals are being urged to ignore any request to host 11-plus exams next month.
The first paper is due to be held on January 9 but there are concerns about bringing hundreds of pupils together in grammar schools.
Education Minister Peter Weir has appealed to primary heads to get involved.
He said they could "make it a reality that children can sit the transfer test in their own primary school setting".
Some grammar schools have already cancelled their exams.
Unions are angry and have accused Mr Weir of laying the groundwork to blame principals should the tests still have to be scrapped.
The INTO said it opposed any move to put the responsibility for unregulated tests into primary schools.
Analysis: `Save the 11-plus' plea causes apoplexy among primary heads
"As the minister has pointed out previously, his department has no control over this process, and INTO has been opposed to academic selection as a means of transfer for pupils from primary to post primary school for half a century," he said.
"To now expect primary schools to take on the facilitation of these unregulated tests would involve schools to facilitate continued social and economic division.
"INTO will be instructing our members to ignore any request from the Department of Education to facilitate this non-statutory testing on behalf of private companies. INTO considers that, in the middle of a Covid-19 pandemic, that the Department of Education would be better served focusing on preserving the health and well-being of the children in their care rather than safeguarding the profit margins of private businesses."
Dr Graham Gault of the National Association of Head Teacher was furious.
"Let's not pretend that this is about children. To create this pseudo moral pressure on primary school principals to resolve a mess for which they have been calling for an alternative, for so many months, is just shocking," he said.
"With three weeks to go, two of them closure, it's hard not to see this as more of a laying-the-groundwork-for-blame exercise than a genuine search for a solution. A genuine search for a solution would have started in April, when primary school leaders were calling this out."
Unions were also unhappy about receiving a letter from Mr Weir late on Friday night informing them that schools would be reopening in January.
NASUWT National Official Justin McCamphill said it was "incredulous that the minister has chosen to email school principals at 8pm on the last day of term".
"Teachers have lived in fear over the past few weeks as infections increased in schools and across the community while there was no intervention prior to Christmas to help reduce the R rate," Mr McCamphill said.
"We now know that Covid will spread rapidly until the 26th December while schools are due to return on the 4 January - this is a disaster waiting to happen. It is an inevitability that education will be disrupted in January as students and staff test positive and colleagues need to self isolate.
"A delay to the full reopening of all schools, coupled with a shift to remote and blended learning in areas of high virus transmission and the roll out of routine testing is the sensible and responsible course of action to protect the welfare, safety and health of pupils, the education workforce and wider community, and also to minimise the disruption to pupils’ learning."
