63 allegations at 17 midlands schools were revealed in a landmark report earlier this week.
The Taoiseach says compensation for those abused in religious-run schools cannot be "parked" until after a full statutory inquiry is completed.
The landmark report revealed 63 allegations of sexual abuse at 17 schools in the midlands, over a period of 30 years.
Nationally, the number of allegations surpasses 2,300, and involves 308 schools.
Speaking during his trip to Ukraine, Taoiseach, Simon Harris, says we have to move forward in a survivor-centred way:
While the Tánaiste says religious orders have a huge responsibility in relation to redress for victims of sexual abuse in their schools.
The scoping inquiry also recommended a redress scheme be established for the survivors involved.
Michéal Martin says justice for the victims shouldn't be delayed:
Gardaí are encouraging anyone who wishes to report a crime relating to historical sexual abuse in schools run by religious orders to come forward.
They say they're fully aware of the profound impact of such abuse - and any reports will be dealt with in a sensitive matter.
Reports can be made by email, by phone or by contacting your local Garda station.
If you feel affected by the contents of the article, One in Four provides supports to adult survivors of childhood sexual abuse. They can be contacted on 01 662 4070 or by completing the form at www.oneinfour.ie/contact.
The Garda Commissioner says officers are investigating whether school abuse was organised and co-ordinated.
A Commission of Investigation will now take place while Gardaí are appealing for victims to come forward.
Justice Minister Helen McEntee says the religious orders would need need to contribute significantly to any potential redress scheme:
Read more: Fears Number Of Sexual Abuse Allegations In Midlands Schools 'Underreported'