The pro-independence Caledonian Union has decided not to choose any of the two rival candidates for president of the territorial Government.
It had earlier said it would make a decision this week as to who should lead the administration to end a political deadlock amid the anti-independence parties, which has left New Caledonia without a properly constituted Government for more than 100 days.
Both Philippe Germain of the Caledonia Together Party and Cynthia Ligeard of the Front for Unity have been vying for the top job, but neither can get a majority within the anti-independence camp.
Caledonian Union leaders say there have been passionate debates, but they have opted to seek collegiality and solidarity to overcome the impasse.
Under the Noumea Accord, both sides are in Government in proportion to their respective strength in Congress.
The French Government has repeatedly implored the loyalist camp to seek a dialogue to overcome differences within its factions.
The crisis erupted in December when the Caledonia Together Party pulled out of a power-sharing deal and brought down the Government half a year into its five-year term in a dispute over fiscal policies.
Several parties have suggested that fresh elections may be needed if the deadlock persists.