The Cook Islands government says the New Zealand government has misunderstood the nature of the Cook's National Superannuation Fund.
There is concern in the Cooks that people who qualify for the New Zealand pension and who also contributed to the local scheme will face deductions.
This follows the New Zealand fund being made portable for those Cook Islanders who satisfy the requirement of having lived in New Zealand for five years after the age of 50.
But the Cooks finance minister, Mark Brown said his country's fund is not a government pension.
"We will be talking to the New Zealand Government in the very near future regarding our particular Cook Islands National Superannuation Fund, and pointing out that it is not a fund that is owned by the Government. It is a fund owned by the members, by the contributors themselves."