Both defence and prosecution sought suppressions in the case after Open Justice applied to photograph the man.
Defence lawyer Tua Saseve sought name suppression for the defendant due to health concerns, while the prosecution raised the issue of automatic suppression for the victim because she was under 18 at the time of offending.
Judge David McNaughton granted interim name suppression but said he would need good reasons to continue denying full media reporting, saying there was strong public interest in the case.
"If the issue is your health then the court will need to see documents supporting the claim," Judge McNaughton told the defendant.
Responding to Crown prosecutor Aminiasi Kefu's point about the victim's young age at the time of offending, he said, "But she's not a child now".
The court also heard Kefu request three months to obtain witness statements from Australia.
The defendant pleaded not guilty at his first appearance in the High Court at Auckland before Justice Sally Fitzgerald earlier this month.
The warrant for his arrest was issued by the High Court in 1997, but "the legislation and the landscape has moved on since that time" and now the District Court is a better fit for the case, Justice Fitzgerald said.
She transferred his case to the Manukau District Court.
"The man had outstanding warrants to arrest in relation to sexual offending charges that were laid in court in 1996," a police spokesperson said.
However, police files on the case were destroyed some time ago due to the passage of time, and exhibits from the High Court had to be released for police to make copies for the reopening of the case.
The case will be heard next on June 29.