And there was little victims could do, short of changing their number. That would not necessarily be a long-term solution, as the scammer appeared to randomly select numbers - possibly through online phonebooks - and could well target the new number.
One Wellington man said his household had received a number of the calls, usually early in the morning.
Today they came about 3 and 4am.
"Phone calls in the middle of the night don't usually bring good news, so you're instantly wide awake," he said.
"It's great there's no bad news but it's extremely annoying to be woken like that."
He had considered blowing a whistle - loudly - down the phone but Telecom advised against that, saying the scammers had been known to either increase the frequency of their calls or abuse their victims.
"Unfortunately it is just one of those things - we do ask customers to call us and tell us," the spokesman said.
"We would just advise to hang up straight away."
A Ministry of Consumer Affairs spokesman said it had received 1700 reports of phone scams this year.
"It appears that as New Zealanders have become educated over the signs of an email scam, scammers have begun cold-calling instead," he said.
"Phone scammers can be considerably more intrusive, persuasive and, in some cases, aggressive. Always be suspect when someone calls you out of the blue and be aware that they may not be who they say they are.
"Never give out your personal details to someone you do not know and remember that you have the power to hang up in a phone conversation."
