The five northern Pacific states, Palau, Nauru, Kiribati, the Marshall Islands and the Federated States of Micronesia, vowed early last year to pull out of the organisation.
They were angry their nominee for secretary general, Marshall Islands diplomat Gerald Zackios, had been overlooked in favour of Cook Islands Prime Minister Puna.
The spokesman for the FSM government said the Micronesian states have been given an undertaking by both New Zealand Prime Minister Jacinda Ardern and Australia's Foreign Affairs Minister Marise Payne that Mr Puna is to step down by June.