"It's irresponsible, totally. It's one thing to hack, but to simply spread the information without any concern whatsoever for the accuracy of the list is totally irresponsible."
Asked if the family had any military ties, the father said he had worked for the New Zealand Defence Force in a non-combat capacity.
"But that has no connection to the Islamic State or serving in a combat role overseas," he said. "It doesn't make sense. There's really no connection between the number that's appeared and my time in the Defence Forces."
The father told 3 News his son was wary of the threat.
"He's holding up as well as can be expected but obviously he's looking over his shoulder," he said.
The New Zealand Defence Force referred questions to the Defence Minister, Gerry Brownlee, whose spokesman said he would not be drawn on why the New Zealander had been targeted or how at risk they were, but one of Isis' tactics was to create uncertainty and fear.
Prime Minister John Key has previously warned Isis was directly reaching out to disillusioned New Zealanders and encouraging them to carry out domestic attacks.
He described this approach, often aided by sophisticated social media campaigns, as a "direct threat on the public of New Zealand". Security agencies have said they closely watch between 30 and 40 people in New Zealand who are considered possible risks as extremists.
Mr Key said details on the Isis list were "scant" and he was relying on further information to be provided to him by officials.
"This isn't the first time we've seen Isis try and use intimidation tactics, in fact it's quite consistent with what they do," he said.
He told reporters yesterday that how real the threat was for the Aucklander named was "relatively unknown". Protection was an option for the family and the individual named.
"The police are looking at the matter and, as and if required, the appropriate support would be put around the person."
The risk to Kiwi troops in Iraq had not changed, he said. "There are always risks operating in Iraq but I don't think they've changed as a result of the list that's been published."
Mr Key wouldn't say whether New Zealand's involvement in Iraq was behind the Kiwi being named on the list.