New Caledonia's Palika party has proposed making New Caledonia an independent state in partnership with France.
The idea was repeated at its Congress at the weekend when it and three other components making up the FLNKS pro-independence movement had separate meetings to discuss the path to next year's independence referendum.
The option proposed by Palika would entail granting New Caledonia a seat at the United Nations.
Another FLNKS faction, the Caledonian Union, said next year's referendum should go ahead, thereby ruling out suggestions of a further accord.
The four separate party meetings followed the Paris talks earlier this month when the Noumea Accord signatories reached agreement on who will be eligible to vote.
The debate in New Caledonia will be given a fresh impetus at the beginning of December when the French prime minister Edouard Philippe is due for a three-day visit.