A caller name-dropped the Prime Minister when offering a Napier couple $5000 "for being good citizens".
They were was flattered but unconvinced yesterday.
Lynne Trafford said her husband Tony answered the call on Wednesday morning and a male with an unidentified foreign accent said John Key had a reward for him.
"The caller said because we had been good citizens and never been bankrupt or in financial trouble, John Key wanted to give us $5000.
"While I'm happy to put my hand up and say they are right - we have never been bankrupt and we consider ourselves good citizens - how on earth could they know that and where have they come by that information?
"Yes, $5000 would be lovely, but it was obviously a scam and Tony hung up on the caller."
Tony Trafford said it was "an interesting conversation", which he speedily brought to an end.
"Afterwards I thought maybe I should have listened longer and tried to find out a bit more, but the mere fact he was offering something for nothing - and in the name of the Prime Minister no less - was enough to render the whole thing unbelievable."
Lynne Trafford said their first thought was to warn others.
"A worrying thing is, are they targeting older people? Tony is in his 80s but he wasn't fooled for a second. What about the next person?"
Police have urged people to be vigilant after the re-emergence of phone scams from callers claiming to be from government departments.
Callers have demanded money in the form of vouchers and made concerning threats to victims should they not transfer funds.
In recent telephone and email scams, people have been told they will get a tax refund if they provide their credit card details and another sent people a link to a false website where they are asked for money and to provide personal information.
NZ Police chief information security officer Paul Blowers said: "These calls can appear fairly legitimate if the caller knows your name and telephone number, but police wish to assure the public that threatening behaviour would not be made from a real government agency caller.
"It is relatively easy for any scammer to obtain somebody's name and phone number. A simple whitebook query, checking social media online or by social engineering means, such as convincing a friend of a friend to reveal some details."
He said police were not able to track callers directly but depending on how they had configured their mobile phone, some details could be revealed - however, they could also easily be hidden.
Prime Minister John Key was unavailable for comment.