A Kanak party wants to enter into a direct dialogue with France to work out the decolonisation process, suggesting New Caledonia become independent, but associated with France.
A referendum on attaining full sovereignty is due on 4 November, ending the 20-year process of the Noumea Accord of gradual transfer of powers.
Discussions about the referendum's aftermath, begun within a small leadership group, have been fraught because of tensions among anti-independence politicians.
Some of them have again walked away from the talks held at the behest of the French prime minister.
Jean-Pierre Djaiwe of the Palika party said he wanted his party to enter into direct talks with Paris to advance the decolonisation dialogue while the political right is caught up in a dialogue of the deaf.
The anti-independence side's latest trouble centers on efforts to determine the values shared by all of New Caledonia's communities.