The New Zealand Prime Minister, John Key, says he is not planning on having another discussion on UN membership with the Cook Islands Prime Minister, Henry Puna.
Mr Puna said this week that the Cook Islands government has not moved on in its hopes to become a member of the UN.
Henry Puna said he plans to continue talks on United Nations membership with John Key when Mr Key visits Rarotonga in August.
However, a statement from a spokesperson for the Prime Minister John Key, says while Mr Key is looking forward to his next conversation with Prime Minister Puna, he is not planning another discussion on UN membership with him.
The statement says Prime Minister Key was clear that New Zealand is not in a position to support Cook Islands membership of the UN under the Cooks Islands' current constitutional status.
The statement says if the Cook Islands wants UN membership, the constitutional relationship, including the current shared citizenship will need to change.
It says New Zealand is open to reviewing its relationship with the Cook Islands, if the Cook Islands wants to do so, though New Zealand is not seeking a change.
The Cook Islands secretary of Foreign Affairs says the country seeks UN membership because it feels its voice can add value to the debate that takes place at the UN.
Myra Patai says independence has never been on the table in terms of the Cook Islands UN aspirations, and there is nothing about having separate citizenship in the criteria for joining the UN.
Myra Patai says there are a number of issues of national importance at the UN table, like fisheries and marine resources, that the Cook Islands would like to add its voice to.
"I think we enrich the debate by bringing our own voices to the table. We have the experiences that will allow us to shape the debate a bit more intimately than New Zealand. Also we have evolved to the point where we are capable, and we already are conducting our own foreign policy separate to New Zealand."
Myra Patai says the Cook Islands is already a member of some UN specialised agencies, and UN membership is the next logical step.