Ministry of Marine Resources Acting Offshore Director Andrew Jones said the operation is taking place in local and international waters.
In addition to the Cook Islands, Jones said French Polynesia, France and New Zealand are also contributing to the mission.
The latter two countries are providing aerial support, with France also contributing a vessel to the operation, he said.
A number of observers reported seeing a RNZAF Orion on the tarmac at the weekend, however, it has not been confirmed if the aircraft is involved.
Lieutenant Commander Tony Grubb, the New Zealand Maritime Surveillance Advisor for the Cook Islands Police, said further comment will be available upon completion of the mission, with dates yet to be confirmed.