38-year-old Dundalk woman Lisa Smith has spent the night in Garda custody in Dublin.
She was detained on her arrival at Dublin Airport yesterday and is being held for questioning, while her child is in the care of relatives.
Justice Minister Charlie Flanagan says all relevant State agencies are involved, and the Tánaiste said it is up to the DPP to decide what happens next.
Lisa Smith came home to the glare of the media and a social media frenzy, and was promptly arrested.
After leaving Ireland to join the so-called Islamic State group, she was detained in Syria, deported from Turkey, and her child taken into the care of relatives on her arrival back in Ireland.
The Department of Foreign Affairs said it first became aware of the case in March when Unicef was warning of high mortality rates at the Syrian camp where the mother and child were being held in "dire conditions" after a Turkish incursion.
Tánaiste Simon Coveney said their primary concern was ensuring the safety of a two-year-old girl caught up in a warzone, adding the DPP will decide what happens next.
“We have been working with partners to ensure we could respond, a complex consular case, primarily the safety of a two-year-old girl in a war zone, living in camps where there have been high instances of child mortality,” he said.
“So we have been, quietly and professionally working to secure the welfare of the child with the help of the Turkish authorities, who insisted on returning them to Ireland."
Asked about public concern about Ms Smith's return to Ireland and her now “living among us”, Mr Coveney retorted by saying: “She is not living among them, she is a garda station being questioned.”
