Government agencies referred media inquiries to other agencies, including to police, Internal Affairs, the Department of Prime Minister and the Cabinet, the Ministry of Foreign Affairs and Trade, and Chris Finlayson, the Minister for the Security Intelligence Services (SIS) and the Government Security Communications Bureau (GCSB).
The New Zealand Intelligence Community, which is responsible for the SIS and GCSB, said: "We are aware of the story, but would not comment on what may or may not be operational matters."
Security analyst and political scientist Dr Paul Buchanan said the case reminded him of earlier cases of criminals using shell companies registered in New Zealand.
Dr Buchanan said it was puzzling why Iceland seemingly uncovered the Auckland connection before local authorities did.
He said local agencies had extensive powers under the GCSB and Telecommunications (Interception Capability and Security) Acts to monitor internet traffic.
"And of course as members of Five Eyes they're privy to all the mass data collection that goes with Five Eyes through Prism and those other metadata collection devices," Dr Buchanan added.
"They may say some things slip though the cracks, although they probably don't want to say that too loudly."
Gareth Foster, Private Box managing director, said he was "horrified" the website was registered to his company. It was believed to have been online since mid-September.
Meanwhile, Dr Buchanan said it was likely New Zealand's SAS soldiers were preparing for battle with Isis.
"The SAS is almost a sure thing. I would be very surprised if they haven't already pre-deployed into the theatre to get ready for the mission."
Dr Buchanan said engineers, medics and possibly an infantry company could join the SAS.
Isis has urged zealots to carry out "lone wolf" attacks against Australians and citizens of other "crusader nations" supporting the military mission in Iraq.
A summit of military commanders from the US-led coalition against Isis, including New Zealand, will meet in Washington today to discuss ways to halt the jihadist group's advance in Iraq and Syria.
Who oversees website domain names here?
The Domain Name Commission authorises registrars, administers a dispute resolution service, and handles complaints about registrars not abiding by ".nz" policies, including incorrect domain name registration.
Why did the Khilafah group choose an .is address?
The khilafah.is domain was registered with Iceland's web hosting service ISNIC. Virtually any person or business can register an .is domain. ISNIC managing director, Jens Petur Jensson said he suspected the domain ending .is was attracting Isis and its supporters.
How often does Iceland delete domain names like the Isis one?
Icelandic media said ISNIC hosted around 50,000 domain names and this is the first time it has deleted a domain.
- additional reporting Sophie Ryan and Patrice Dougan of APNZ, and Lincoln Tan of the New Zealand Herald
