Transfer tests should be pushed back until after Christmas, an MLA has said.
On Monday, Education Minister Peter Weir announced post-primary tests would be delayed by at least two weeks, until late November and December.
But Ulster Unionist Robbie Butler, who sits on Stormont's Education Committee, said he was "astonished" they weren't being held off for longer.
The Lagan Valley MLA said parents, particularly key workers, were worried their children would be at a disadvantage.
He added: "Everybody, from head teachers in my constituency, they're supportive of it being delayed by a much greater extent.
"Frontline workers who are working long hours who really feel like they're not giving their kids any educational support at the moment feel like their kids are going to miss out."
Tests run by AQE will be taken on three Saturdays - November 21 and 28 and December 12. Those provided by PPTC will be held on December 5.
Mr Weir said: "It is back to the issue around transfer, that we have a range of schools which are over-subscribed.
"Those schools are entitled, if they so wish, to use academic selection."
He added there had to be a timeframe enabling pupils to be able to transfer schools successfully.
Earlier this week, Alliance MLA Chris Lyttle said the pandemic meant it was "time to find a different way to transfer pupils from primary to post-primary, so we can leave the unfair and unnecessary transfer tests in the past where they belong".
Speaking in the Assembly, he asked the Executive to intervene.
Addressing the First and deputy First Ministers, he asked: "How it is right to require 10-year-old children to sit those transfer tests in November and December… when the Executive can take action to change the use of these tests for post-primary transfer admissions?"
In response, DUP leader Arlene Foster said the majority of parents wanted academic selection, and "we believe that should be facilitated".
Mr Weir also said yesterday that remote learning needs to be as consistent as possible.
He praised teachers for their efforts to deliver lessons online while schools are closed.
Mr Weir told the Committee for Education: "We want to ensure there is as much consistency between schools as possible.
"Work has gone on, teachers have gone above and beyond."
A roadmap out of lockdown published by the Executive on Tuesday said schools will not fully reopen to early years pupils until the fifth and final stage.
Schools are open to vulnerable children and children of key workers, and the roadmap envisaged that would be expanded to cover a wider definition of key workers as workplace activity gradually increased.