Lisa Smith is to be questioned for a further 24 hours after her period of detention was extended by a garda chief superintendent this morning.
The former member of the Defence Forces is being questioned by gardaí at Kevin Street Garda Station in Dublin.
The Co Louth woman travelled to Syria in 2015 to join Islamic State after converting to Islam several years before.
She can be questioned for up to three days by the authorities.
Gardaí say her child, who arrived back in Ireland with her, is being cared for by relatives.
Ms Smith was offered the opportunity to rest overnight.
Minister for Justice Charlie Flanagan has described it as "a sensitive case" and said he wanted to reassure people that all relevant State agencies were closely involved.
Detectives are interviewing her under caution about her activities, movements, communications and contacts online and in person in Africa, Europe, the Middle East and Ireland since she converted to Islam several years ago.
The legislation that allows gardaí to prosecute someone for terrorist offences abroad remains untested.
It will be for the Director of Public Prosecutions to decide if Ms Smith is to be charged or released.
However, as well as the criminal investigation gardaí are also carrying out a security assessment on Ms Smith, as they have done in the case of five other people who have returned from conflict zones, so that they can be satisfied the Dundalk woman does not pose a threat to the security of the country.
Her solicitor has said "it is too early" to tell if a file will be sent to the DPP.
Darragh Mackin said he is of the view that the evidence is very weak and Ms Smith has a very strong case to make.
Speaking on RTÉ's Morning Ireland, he said his client had categorically denied being involved in terrorist offences and it was "unprecedented" for someone to publicly disassociate themselves from IS, as Ms Smith did while she was in a camp in Syria.
Mr Mackin said: "We are of the view that the evidence of the State is inherently weak and does not point to terrorist offences. As such, we believe that Lisa has a very, very strong case to make and is currently making that case."
He said "not one witness has come forward" to back up allegations that Ms Smith engaged in terrorist activities and until such time that someone does, the allegations were hearsay.
In an interview with RTÉ News earlier this year, Ms Smith explained why she joined the caliphate, a self-declared Islamic State that once covered swathes of Iraq and Syria.
"I run with the crowd," she said.
At its peak IS militants imposed a brutal rule on millions of people. Members followed sharia law, a radical form of Islam from the eighth century.
IS soldiers kidnapped, raped, murdered and beheaded those who broke their strict rules.
Ms Smith has acknowledged the brutality but has denied being a member of IS or to have engaged in active fighting.
She said she never carried weapons for the militants or trained young girls as young as nine in how to use weaponry.
