Calls might also appear to come from an 04 (Wellington) or an 09 (Auckland) prefix.
People should be aware New Zealand government agencies such as Immigration or Inland Revenue would never call, email or text demanding payment or threatening deportation, police said.
Banks would never call and ask for online banking passwords. These agencies would also never use money transfer services such as Western Union.
"Our advice to anyone who is targeted by this scam is to hang up immediately," Mr Glossop said.
"Warn others and prevent your friends and family from becoming a victim of this scam."
Reports of people being targeted in the Tasman area are also emerging.
Police advice
• Hang up immediately.
• If it doesn't seem right, be cautious, double-check details first.
• Do not pay money to anyone you have never met.
• Look after your personal details in the same way you would your wallet and other possessions.
• Be aware of common scams. For example, banks, Immigration New Zealand or Inland Revenue never email, call or text customers to ask for money to be sent using money transfer services.