The French high commissioner in New Caledonia, Albert Dupuy, has begun three days of consultations on changing the 1999 law governing elections.
All political parties and leaders of the territorial and provincial administrations are invited ahead of further discussions in Paris next month, called by the French prime minister.
The planned law change is aimed at the Caledonia Together Party which quit the collegial government three times within a month to provoke Paris to call fresh general elections.
To avoid further resignations, the Congress has suspended any elections which under the current law have to be held two weeks after a government collapse.
The resignations came amid Caledonia Together's call for the territory to choose a new flag.
However, a majority of Congress members and the French government have opted for the joint use of the French and Kanak flag.