Acting Senior Sergeant Chris McLellan, of Dunedin, said police had received several reports from people who had received such phone calls.
The caller then asked for a credit card number to take a processing fee, and the person never heard from them again, he said.
The Otago Daily Times is aware of at least one elderly woman who had hundreds of dollars removed from her account after giving her credit card number to the caller.
Anyone receiving unsolicited calls should always exercise caution and common sense, Acting Snr Sgt McLellan said.
People receiving the calls were advised to note all relevant details, refrain from providing personal information such as bank account numbers and family details, never meet payment demands, and report the matter to police immediately.
The Consumer NZ website includes further information on how to protect yourself.
AMI yesterday warned people to be wary of calls from people claiming to be from AMI and asking for sums of $10,000 to $25,000 for investment purposes.
To date there had been 26 reported cases.
AMI chief executive John Balmforth said the calls had nothing to do with AMI Insurance.
"We do not sell investment products.
"Anyone receiving such an unsolicited call claiming to be from AMI and trying to sell an investment should terminate the call and notify us," Mr Balmforth said.
