She was speaking at the Northern Ireland Assembly’s education committee on Friday.
Her comments come after a teaching union, the NASUWT, called for a staggered return to school for pupils following the Christmas break.
The union made the call in a letter to the minister, after earlier calls for an early closure from its top Northern Ireland official Justin McCamphill — made in a BBC radio interview — were shot down by the minister.
Addressing the committee on Friday, Ms McIlveen said: “I recognise that Omicron is taking us into a new phase of the pandemic and we need to remain vigilant.
“The Executive’s priority remains keeping our children and young people in school.
“I will therefore continue to work with all concerned to keep our schools open and safe.”
She continued: “You’ll be aware that there is a high number of covid cases in the community and in schools.
“The advice from the department of health is that the case rates in schools reflect the prevalence in the wider community.
Transmission is occurring both in the community and in schools.” On the potential risk posed by the new variant, she said: “There is also much that is not yet known about the potential impact that the omicron variant might have both in society and in schools.
We all await further scientific conclusions before being drawn as to how it may change the current picture. My department will be able to respond as required if the need to do so arises.”
She added: “The Public Health Agency publishes detailed weekly statistics on the cases found in schools as part of its bulletin. The most recent bulletin covers statistics for the four weeks up to the 12th of December.
“In broad terms, it’s clear that among a largely unvaccinated school-age population there are currently a high number of cases. The PHA report references that in the seven days up to the 12th of December there were 3,405 cases in schools including staff and pupils.”