New Caledonia's pro-independence Caledonian Union says it will present a proposal to end the political deadlock within two weeks.
The territory has been without a president for more than five weeks after the administration of Cynthia Ligeard collapsed amid disagreement within the anti-independence coalition.
Two attempts to elect a new president have failed, leaving the government in caretaker mode, with none of the three anti-independence parties prepared to alter their position.
The anti-independence side has six ministers and the pro-independence side five, who have abstained in the election.
A Caledonian Union leader has told the local newspaper that a plan to end the crisis is being discussed and will be aired at party congresses this and next weekend.
A leading anti-independence politician, Philippe Gomes, says if the impasse continues, a fresh general election needs to be called.