Police say they have received calls from people who have found infant formula products that may have been tampered with - including some with possible pinpricks in the lids.
They said a number of tins of product had been collected and were being forensically tested, and all information relating to the incidents was being assessed.
Police said there was no information at this stage to suggest the public was at risk.
They said people should still be vigilant when buying infant formula and check all products for tampering.
Infant formula threat: More information
The update follows the announcement by police on 10 March that they had spent more than three months investigating a blackmail threat to poison New Zealand milk products.
Fonterra and Federated Farmers were sent a letter each in November containing a blackmail threat and powder. It tested positive for concentrated forms of 1080.
The author threatened to poison the infant formula supply chain at the end of this month, if New Zealand didn't stop dropping the poison in the wild.
An investigation team, dubbed Operation Concord, has been set up and is working with the Ministry for Primary Industries (MPI) to identify who is responsible.
Shortly after the threat was made public, MPI deputy director-general Scott Gallacher said the ability for anybody to contaminate infant formula during manufacturing was "extremely low".
He said new testing measures in partnership with retailers had checked 40,000 raw milk and product samples and no 1080 had been found.