Gardai said they have successfully identified the teenage girl after releasing a photograph of her.
They will be "liaising closely" with Australian police.
Her name and age have yet to be revealed publicly.
She is believed to be 19-20 years old.
"With the assistance of the public, the Gardaí are now following a definite line of enquiry and will be liaising closely with the Australian Police and the HSE to finalise the matter," a Garda spokesperson said this evening.
"Gardai wish to sincerely thank the public and the media for their assistance. They also wish to inform them that no further assistance is required at this time," they added.
This morning, they released the first picture of the child found in Dublin that gardai suspected was a victim of human trafficking.
All efforts to identify her have failed, leaving officers with no option but to make a media appeal.
The girl was initially believed to be aged between 14 and 16 and was found wandering outside the GPO four weeks ago.
She did not speak clear English but has drawn pictures for officers and healthcare workers of being taken by men on an aeroplane and also being placed on a bed and lying with men.
Last week, the case went to the High Court as gardai attempted to obtain permission to release her photograph in order to try and identify her.
Now her picture has been released in an attempt to identify her.
The investigation was given the name Operation Shepherd.
To date it has involved over 2000 man hours and 115 separate lines of inquiry.
Fifteen possible names were provided to investigators. But when these were fully checked, they proved to be incorrect.
The investigation has involved door to door enquiries, on street vehicle and pedestrian checkpoints near where the girl was discovered, the seizure and viewing of CCTV.
Juvenile liaison officers throughout the country canvassed with images of the girl as did gardai attached to child protection units. Social youth workers and homeless services were also contacted.
Images of the girl were distributed on the internal garda computer system, checks were made at ports, airports and train stations.
Bed and breakfasts and guesthouses in the city centre were also checked.
The girl was found wearing braces and paediatric orthodontists around the country were canvassed.
However, no information which might identify the girl was found.
Garda spokesman Superintendent Dave Taylor said the investigation "has not brought us to the point where we can identify this child."
He said gardai believed she is European.
"But from where in Europe we cannot say," said Supt Taylor.
She is described as being 5ft 6ins in height, of slim build and having long blonde hair.
When found she was wearing tights dark coloured jeans, flat black shoes and a grey woolen jumper.
Gardai believe the clothes were bought from retailers in Ireland.
"My appeal today centres on who may recognise the girl from the photo. Do you recognise this girl? Did you have any interactions with her? Did you pass her in a distresed state in the city centre in and around October 10," said Supt Taylor.
"Any information is vital to the investigation, and the welfare of the child."
Orla Ryan, Guardian Ad Litem, said: "I am extremely concerned about the welfare circumstances of this young person. What we know about her, at present, is limited. It is in the child’s best interests to be identified, and I fully support An Garda Síochána in their continuing investigation.”