Judge Stephen Coyle - despite accepting the mother unlawfully took the girl and concealed her - refused because she was now settled in New Zealand, as first reported by the Herald.
Doing so would be an "intolerable situation" and "cataclysmic" for the girl, said Judge Coyle, and returning her was not in the child's best interests.
His ruling on the Hague Convention application was upheld on appeal to the High Court last year.
"The predictable effects of an order for return are much more than tears and mere physical and emotional upheaval," Justice Davison wrote last June.
"Here the effects of an order for return will be harmful and damaging, with potential lifelong consequences."
But the High Court judge pointed out his decision should not be taken as condoning the mother's actions, which he described as an "egregious breach" of her legal obligations.
"Rather, in this case Anna's welfare and best interests - as evident from the fact she is so well settled in her present life in New Zealand and has so firmly expressed her objection to returning to [Europe] - outweigh the policy provisions of the [Hague] Convention."
But the matter is far from settled after the Court of Appeal today agreed to hear the case.
In a decision released today, Justice Murray Gilbert said the original decision of Judge Coyle relied significantly on the evidence of the court-appointed psychologist.
"The [father] is particularly critical of the psychologist's evidence, which formed the primary evidential foundation for the key factual findings.
"The [father] has made a formal complaint to the New Zealand Psychologists Board, which has determined that there is sufficient substance in the complaint to warrant referral to a professional conduct committee for further investigation."
Now the Secretary of Justice, as the Central Authority for New Zealand under the Hague Convention, has sought leave to intervene in the father's appeal because the case raises issues of public importance.
"This is because there is an expectation of uniform judicial interpretation of the Hague Convention amongst signatory States so that the objectives and purposes of the Convention are fulfilled."
Justice Gilbert said the appeal lodged by the father should be heard by the Court of Appeal as it raises "questions capable of bona fide and serious argument".
"The case involves questions of considerable private and public importance that in our assessment outweigh the cost and delay of a further appeal."
The father is at a loss to explain why his former partner went to such lengths to cut him out of his daughter's life.
"All I want is to be part of my daughter's life. A child needs both parents."
The courts in their home country awarded sole custody to him after the mother repeatedly refused to let him see their daughter.
"The ingrained resentment the mother holds against the father, now significantly impairs the mother's ability to raise her daughter ... with her actions, the mother wilfully and significantly disregards the interests of her daughter," the European court judgment said.
The girl's mother has repeatedly declined to comment, although claimed in court documents the custody battle was "vexatious" and "relentless harassment" which made their lives "unbearable".
The global "tug-of-love" battle also ended up before the Immigration and Protection Tribunal, which cancelled deportation notices issued by Immigration New Zealand.
Deportation would have been "unduly harsh" and unjust, ruled the tribunal, despite the mother concealing relevant information to obtain a visa and illegally removing the girl from her home country.
"If the family can stay in New Zealand at this stage, this will at least maintain the daughter in her current family life, which the Family Court has held to be in her best interests," said the tribunal.
"The issue of contact with her father and the associated emotional turmoil can no longer be avoided, but, if the daughter is in New Zealand, it will be for the Family Court to determine if and how the contact will take place."
The tribunal also discussed the father taking the girl from her New Zealand school, with a "child recovery team" of private investigators from Australia, after the original Family Court ruling.
This was an abduction, according to the mother's submissions which had created "extraordinary stress and fear".
In response, the father said he took the extraordinary step to re-establish contact with his daughter, whom he had not seen in nearly five years.
In the High Court ruling, Justice Davison noted the only custody order in place for Anna was the one issued by the European court, which noted the mother's conduct showed she would not release her daughter without "direct force".
However, the trauma of being taken from school reinforced Anna's objection to being returned to her father.
Justice Davison took her opinion into account when balancing her welfare and best interests against the deterrent policy of the Hague Convention.
Generally speaking, the "abducting" parent should not gain an advantage from concealment or deceit.
In this case, the father did not know where his daughter was for two years and Justice Davison said the passage of time meant the girl "wholeheartedly embraced" her new life.
This also meant the mother could rely on the "settled" defence to keep her daughter in New Zealand, which Justice Davison said was taking advantage of her unlawful conduct in "flouting" the court orders in her home country.
"The respondent's reprehensible actions are the very kind of conduct that the Hague Convention provisions and policies are directed to prevent, and which the courts of all jurisdictions rightly condemn as contrary to the rule of law," said Justice Davison.
"It is important to keep in mind that throughout that extended period, the [father] has been prevented from having any contact whatsoever with his daughter, while the [mother] has had exclusive contact and the opportunity to influence Anna to adopt her attitudes towards the [father], rather than Anna forming her own views independently."
Global custody battle
• February 2017: Application lodged with Family Court to return Anna to her father in their homeland.
• May 2017: Immigration NZ issued deportation liability notice against mother for concealing relevant information in visa application.
• September 2017: Family Court rules girl should not be returned to father in homeland.
• October 2017: Immigration and Protection Tribunal cancels deportation notice and issues new visas.
• June 2018: High Court releases full reasons upholding the decision of the Family Court.
• February 2019: Court of Appeal says case raises significant issues of public interest and agrees to a fresh appeal.
