Scammers impersonating the National Cyber Security Centre (NCSC) are targeting local internet users with demands for personal information.
The scammers allegedly accused computer users of accessing "illegal websites" before making demands.
"It sounded like a cold-calling scam," said Lee Chisholm, Netsafe operations manager.
She understood the scammers asked for money or remote access to computers, and probably targeted victims at random.
Ms Chisholm said people still frequently lost money to scammers, with $13.4 million reported to Netsafe alone last year, but real losses were probably far higher.
She said scams involving people pretending to be from the Inland Revenue Department or offering "government grants" were also widespread.
In November 2014, phone scammers from South Asia promising tax refunds and "government grants" targeted New Zealanders in an attempt to get personal and financial details.
An NCSC spokesperson said the latest con was "a new twist" on a known scam.
Scammers asked for personal information such as a physical address and IP (internet protocol) address.
"We do not contact private individuals or organisations, seeking personal information. This is just another version of known scams where people are contacted by scammers, alleging to be from an official organisation or reputable supplier, in an effort to get access to computer systems or personal information which can then be used for illegal activity," the spokesperson said.