The Department of Education has said that primary schools should "continue their engagement" next week with any parents who do not send their children to school with a mask on Monday morning.
A spokesperson said that in discussions held today, education partners were told that such engagement should "address their concerns and reassure them that the measures are for the benefit of the entire school community".
Talks were held to discuss the implementation of the latest public health advice in schools.
The Department said that more detailed advice, in the form of Frequently Asked Questions, will be sent to schools on Monday morning.
Earlier, a spokesperson for the Department said that mask-wearing for older primary school children was "absolutely" a requirement and not advisory.
This followed comments by Minister of State for Special Education Josepha Madigan on RTÉ's Today with Claire Byrne that the advice was advisory and schools were free to use discretion.
The memo that was sent to schools on Tuesday evening stated that mask wearing for older primary school children is required - apart from children who have specific medical exemptions.
It stated that children who do not have masks "will be" refused entry.
The mandatory nature of the instruction has angered many schools, who have said it is unhelpful and inflammatory.
Schools also have concerns about the legality of turning a child away because their parents do not wish them to wear a mask, and they are highly reluctant to do so.