In a statement, the FAI said it was "shocked and appalled to learn of disturbing allegations of abuse brought forward by women in involved in Irish football in the 1990s."
The FAI said it had met with some of the women to listen to and acknowledge their experiences, while also offering support.
Minister for Tourism, Culture, Arts, Gaeltacht, Sport and Media, Catherine Martin, has described the allegations as "very shocking."
"I have been assured that the Football Association of Ireland, as the National Governing Body for the sport, is engaging and co-operating with the live Garda investigation into these allegations, with an athlete-centred approach," she said in a statement on Thursday evening.
"I commend the bravery of the women who have stepped forward," she added.
In its statement, the FAI said it has contacted the gardai and Tusla about the cases, in accordance with mandatory reporting requirements and its own safeguarding and child welfare regulations.
"The Association acknowledges the enormous courage of the women in coming forward and making their concerns known and would encourage anyone involved in Irish football to report any concern that may arise," it said.
"The Association believes unequivocally that everyone involved in Irish football should at all times feel that they are in a safe environment and that appropriate safeguarding and reporting processes are in place and operating effectively."
The Professional Footballers Association of Ireland (PFAI) has been providing support to the women over the last six months.
The FAI has asked that anyone who experienced harm or abuse from Irish football to contact an independent contractor it has hired to take statements from complainants.
The contact numbers for Raiseaconcern are 01 6107929 or 086 0299929. Individuals can also email football@raiseaconcern.com.
Anyone who wishes to contact the team behind the joint investigation with information can contact marie.crowe@rte.ie / mark.tighe@independent.ie
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