Her legal team says she is cooperating with Gardaí.
Lisa Smith has had her period of detention extended to a third day.
The 38-year-old is being questioned as part of a criminal investigation into alleged terrorist offences.
The Dundalk native was arrested on Sunday after she returned to Ireland with her 2 year old daughter on board a Turkish Airlines flight.
Gardai made an application in the District Court today to extend her period of detention by a further 24 hours.
She remains in custody in Kevin Street garda station in Dublin.
Her legal team says she is cooperating fully with Gardaí.