They asked that part of the final report, a case study on Jehovah’s Witnesses, not be published on the Royal Commission’s website, that it be kept confidential and not reported on.
Justice Cooke declined the application in a judgement released on Tuesday, citing “considerable public interest” in the report and the fact they had waited till the “very last moment”.
He also said the chances of their success in the Supreme Court “must be regarded as low”.
RNZ has asked the Jehovah’s Witnesses for a response on the decision.
Justice Cooke noted no affidavit evidence was filed by the Jehovah’s Witnesses in support of the application.
“We nevertheless accept that the appellant has a position to preserve,” he said.
“Publicising the section of the report dealing with the issue of abuse by members of the Jehovah’s Witnesses faith will likely have a reputational impact on the appellant, and the faith more generally.”
He said any subsequent decision of the Supreme Court concluding that it was beyond the jurisdiction of the Royal Commission to make such findings may mitigate that impact, but would not eliminate it.
“Having said that, we do not understand there to be a dispute that the Royal Commission received evidence of abuse engaged in by members of the Jehovah’s Witnesses faith,” Cooke said.
“The appellant’s argument in this proceeding has been limited to arguing that the Royal Commission does not have jurisdiction to investigate and report on that abuse because it did not take place in a relevant “care” setting.
“But we nevertheless accept that the proposed order can be seen as necessary to preserve the appellant’s position.”
Justice Cooke said the report into abuse in care was “a matter of considerable public interest”.
“This has been a long-running inquiry in relation to matters that have had a significant impact on many people’s lives, in particular the survivors of abuse,” he said.
“There would need to be very compelling reasons before it would be appropriate for a court to prevent publicity over part of the report in those circumstances.”
Justice Cooke said it would be wrong to suppress part of the report.
“We consider that a report of this kind likely involves interrelated issues applying across state and faith-based care,” he said.
“The inquiries concerning the Jehovah’s Witnesses form part of an overall story which is properly told in the public interest.”
Last month the Jehovah’s Witnesses tried - and failed - to get an advance copy of the Abuse in Care Inquiry’s final report into their church.
It also unsuccessfully sought all relevant underlying documents supporting the case study.
Jehovah’s Witnesses is the only religious group to take legal action against the commission.
It has taken similar action against public inquiries overseas, including in Australia and the United Kingdom.