Gardaí are studying replies made by returned Islamic State supporter Lisa Smith to questioning as they decide whether to go to court and seek a further extension to her detention.
Ms Smith's solicitor, Darragh Mackin, said his client was cooperating fully with gardaí and answering questions posed by them.
Ms Smith was arrested just before 11am on Sunday after she was flown from Turkey along with her two-year-old daughter.
The former member of the Defence Forces was met at Dublin Airport by the Special Detective Unit officers and taken to Kevin Street Garda Station.
She had been in Syria, in the territory of the so-called Islamic State, since 2015.
She was detained under Section 30 of the Offences Against the State Act, which allows for a maximum detention period of 72 hours.
Gardaí have said they were investigating Ms Smith for suspected offences committed abroad under the Criminal Justice (Terrorist Offences) Act 2005.
There are a range of offences covered under this act, and its mother legislation, the Offences Against the State Act 1939, including: membership of an unlawful organisation; training someone in the use of firearms; engaging in, or attempting to engage in, a terrorist activity or terrorist-linked activity; or public provocation to commit a terrorist offence.
Mr Mackin said his client “categorically denied” any involvement in terrorist offences or terrorist organisations and said that while she went to the geographic and political entity that was Islamic State in Syria, she never joined the militant group Islamic State.
Gardaí have been developing a comprehensive file in relation to Ms Smith, which is thought to include intelligence from foreign security services and statements, including admissions, made by Ms Smith in media interviews.
Sources said the arrest was conducted to put the evidence to her to get her response – and, in turn, to check out those replies.
It is understood senior officers are engaged with the DPP on whether or not to seek a further extension from the district court.
Ms Smith can be held by gardaí for a maximum of 48 hours, meaning that on Tuesday morning they would have to go to the district court to get a final 24 hours' detention.
Sources said they will have to demonstrate to the judge that they need extra time to check out any replies given by Ms Smith and revert to her.
Speaking on RTÉ's Drivetime, Micheal O'Higgins SC said bringing a prosecution in this area was “unchartered territory” and that pursuing charges of a terrorist offence abroad would be “really difficult”.
He said a membership charge would be easier and require “circumstantial evidence” and evidence of a chief superintendent of his belief Ms Smith was a member of an unlawful organisation, with reports of foreign intelligence agencies the basis of that belief.
In relation to the distinction between Islamic State the territory and Islamic State the organisation, he said it depended on which was considered unlawful under the legislation.