Police say more than 900,000 scam phone calls were made from one number in June and July asking people to pay outstanding fines using iTunes vouchers.
Detective senior sergeant Iain Chapman said the phone numbers made the calls appear to be coming from New Zealand, including those associated with Government departments and police.
But he warned that those agencies would never request fines be paid by iTunes vouchers.
"While these numbers may show a New Zealand number, they are in fact coming from overseas," Chapman said.
"We are seeing a huge numbers of these calls coming through, with over 900,000 calls showing as coming from one New Zealand number over the months of June and July.
"It's really important to remember that Government agencies will never require or ask you to pay a fine by using an iTunes voucher.
"If you get a call from someone saying you need to pay a fine by iTunes vouchers, Police's advice is just to hang up.
"We are also seeing a wide range of the public being targeted through these calls, including the elderly.
It's really important to remember that Government agencies will never require or ask you to pay a fine by using an iTunes voucher.
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"If you do have family members or relatives who are not technologically savvy, we do ask that you have a chat with them about this so they do not fall victim to this type of scam," Chapman said.
Police said if people did have outstanding fines and were concerned, they should find the contact details of the organisation from the phone book or their website and use the generic number listed.