In the first four months of the current financial year the FMA received 25 complaints about cold calls, compared with 30 complaints in total for the previous year ended June 30.
The FMA is highlighting the issue as part of International Fraud Awareness Week and said while it was hard to quantify the money involved, it was aware of individuals losing amounts between $4,000 and $700,000.
It said the operations are usually set up by a team of fraudsters in temporary offices overseas - outside of the FMA's reach.
The groups then offer non-existent, worthless or overpriced investments, usually in shares although the FMA said it was aware of FX trading, binary options and sports investment schemes also being sold this way.
As well as being unsound investments, Gregory said the schemes were illegal and the best thing to do was to simply hang up.
"Often the deals through cold-calls and boiler-rooms sound too good to be true," Gregory said.
"We recommend when considering any investment, make sure you do your research, deal with a licensed provider and talk to an adviser if you need to."
The FMA's advice includes never sharing financial details with people you don't know, only dealing with a registered and licensed financial provider and doing your research. If it sounded too good to be true, it probably was, the organisation said.
Bronwyn Groot from BNZ's Financial Crime and Security team said several recent examples illustrated how sophisticated the schemes had become.
"These scams take fraud to a new level - they are incredibly slick operations that target informed, high-value investors," Groot said.
The money loss was huge, including about half a million dollars in just one case of which the BNZ was aware.
With this new type of operation, one of the red flags according to Groot was that it was a pressured sale - much more so than was allowed in New Zealand.
She said urgent or rushed sales tactics should automatically set off alarm bells for investors.
"If you're not sure, do your homework," she said. "Check out the broker, call your bank or the FMA and see if this is a known scam."
FMA's advice
Never share financial details with people you don't know.
Only deal with a registered and licensed financial provider.
Do your research.