The Cook Islands can only have its own passport if it gives up New Zealand citizenship, the office of New Zealand's Foreign Minister, Winston Peters says.
The Cook Islands operates in free association with New Zealand.
It means the island nation conducts its own affairs, but Aotearoa needs to assist when it comes to foreign affairs, disasters and defence.
Cook Islanders also hold New Zealand passports entitling them to live and work in the country.
Prime Minister Mark Brown wants his nation's citizens to have their own passports. He previously told RNZ Pacific he viewed this as an "internal matter" that would not affect the unique relationship between the two nations.
Cook Islands PM seeks to create new passports
However, the office of New Zealand's Foreign Minister Winston Peters said a separate passport, citizenship and membership of the United Nations are only available to fully independent and sovereign countries.
"The Cook Islands cannot access these things while it remains in free association with New Zealand, but could do so if it chose to become fully independent," the statement said.
"Making fundamental changes to the constitutional relationship between the Cook Islands and New Zealand must be decided by the Cook Islands people via referendum.
"Such a referendum would allow the Cook Islands people to carefully weigh up whether they prefer the status quo, with their access to New Zealand citizenship and passports, or full independence.
"If the goal of the government of the Cook Islands is independence from New Zealand, then of course that's a conversation we are ready for them to initiate."
Brown previously said he planned to announce something in 2025 during celebrations of the 60th anniversary of the Cook Islands' self-governance.
A spokesperson for Peters said the current relationship worked well for both sides.
"We deeply value Cook Islanders as New Zealand citizens - including the almost 100,000 who live in New Zealand.
"Cook Islanders are members of our diverse family, with their own distinct cultural identity."