Schools have been urged to comply with a call by the Catholic Principals' Association to suspend academic selection.
Over 200 Catholic head teachers called for transfer tests to be scrapped until next year.
In an open letter, published in the Irish News, they pointed to "the inevitable emotional distress of primary school children during this pandemic" and the gap in teaching. The principals also asked all grammar schools to suspend the tests.
Sinn Fein education spokesperson Karen Mullan welcomed the intervention.
She said: "A growing number of grammar schools across the north have already shown leadership and announced they are suspending the use of academic selection tests this year as a result of the Covid-19 pandemic.
"I would call on the remaining grammar schools which are still intent on using these unfair, unnecessary and unregulated tests to heed this call and abandon the use of academic selection this year and for good."
Unofficial transfer tests have been used since the abolition of the 11-plus in 2008 and are run by private test providers Association for Quality Education (AQE) and the Post-Primary Transfer Consortium (PPTC).
So far, 11 Catholic grammar schools and the integrated school Lagan College have confirmed they will not use the test results to admit pupils in 2021.
The Catholic Principals' Association, which wants a complete end to academic selection, is also calling for the tests to be cancelled in future years due to the impact of the coronavirus.
Its chairman Kieran O'Neill said: "The grammar schools that have already made the decision to suspend the use for this year have led the way.
"And whilst that is to be commended, there are still a number of Catholic grammars and indeed other grammars across the province, that haven't done so.
Mr O'Neill added: "The current Year 5 children have just had something like four months out of school.
"Next year, following the formula suggested by Education Minister Peter Weir, they may have two days in school and two days off school and, depending how long this continues, they will receive 50% of their education for their whole P6 year."