New Zealand had knocked back the government's aspirations for a seat, saying it was not an option if the Cook Islands wanted to retain New Zealand passports for its people.
The Cook Islands 'free association' relationship with New Zealand leaves Wellington responsible for defence and foreign policy and while the Cook Islands had separate membership of some UN agencies it was represented by New Zealand at the main international body.
The Acting Prime Minister Mark Brown said New Zealand citizenship was very important and people didn't want to lose the link between the two countries.
Mr Brown said there were other things the Cook Islands wanted like further relaxing residency criteria for Cook Islanders eligible for New Zealand pensions.
"We would be pushing for that," he said.
"The UN matter for us is something that we'll be looking at more long-term.
"It may come up again in the future for us to pursue but again from our perspective, membership of the UN has got nothing to do with the special relationship that we have with New Zealand."
Photo: Phillipa Webb / Cook Islands News Mr Brown said the Cook Islands are still interested in UN seat