People who are already shares scam victims are being targeted a second time round by fraudsters.
The Securities Commission today said that the overseas callers making the offers were part of a new wave of telephone share scams.
Fraudsters had taken many millions of dollars from New Zealanders in the past decade, particularly targeting people with small businesses.
They were convincing and persuasive, commission director of market supervision John Mulry said.
The fraudsters regularly changed their tactics, their names, and the countries they operated from - to avoid detection and to keep the money rolling in.
It was common for them now to call people who bought bogus shares in one of the earlier scams. This time round they claimed to have a buyer for their shares.
" Do not be tempted to take up these offers, they are all part of the scam," Mr Mulry said.
"Inevitably you will be pressured to send more money."
A list of fraudsters could be seen on the commission's website and the Australian Securities and Investments Commission website.
The lists were not exhaustive, and the fraudsters changed their names often, he said.
If a caller was not on the list it did not mean they were genuine. All unsolicited calls should be treated with suspicion.
More information on telephone share scams was available on the www.sharescams.org.nz website.