The Government said it was worried that a hit list issued by Islamic State naming an Auckland man could encourage a lone wolf attack.
The man was named along with his email, a phone number and other details, in the list of more than 1400.
Prime Minister John Key said he was still determining how real the risks were - but said Islamic State was well known for its intimidation tactics.
"But its one thing to put out a list and it's another very different issue to actually carry that out. Now we don't take those threats lightly, there's a New Zealander named on that list.
"We have a responsibility both to that person, their family and actually to fellow New Zealanders to get to the bottom of it."
Police said they were in contact with the family of the man who was named in the list and were providing support and advice to them.
His parents said they were at a loss to understand why their son's name had appeared on the list as he had no connection with the military or any security service.
Police said they could also find no reason why the man's name was there.
The Labour Party's foreign affairs spokesperson, David Shearer, said New Zealanders were very global and got involved in all sorts of issues - so he said it was not surprising an Auckland man had been named.
"What we've got to realise is that when you see other westerners who have been taken prisoner in other countries, there's going to be a chance that a New Zealander's going to be caught up in there somehow," Mr Shearer said.
He said the threat needed to be taken seriously, but warned security agencies had to be careful that they did not provoke anything, like a lone wolf attack.
"What you have to do is not rule anything out, so therefore you have to take every precaution to make sure that an eventuality like a lone wolf situation doesn't occur," he said.
The Minister in charge of the Security Intelligence Service, Chris Finlayson, said the matter was being treated seriously.
He said they were always concerned that a radicalised person could take action.
Mr Finlayson said if needed, protections could be put in place for the Auckland man named.
But he would not say what that protection would involve and whether the man or his family had requested it.
List not endorsed by IS, says expert
An analyst with Flashpoint Global Partners in Washington DC, Alex Kassirer, told Nine to Noon much of the information appeared to have come from social media.
She said it showed tech savvy Islamic State supporters were opening up a new front using the Internet in efforts to instil fear and chaos.
Ms Kassirer said Islamic State itself has not mentioned or endorsed the list.