A small party within New Caledonia's pro-independence FLNKS umbrella group says talks should be considered with the anti-independence Caledonia Together party to break the political deadlock.
Last week, the formation of a new government failed after none of the 11 newly elected ministers could secure six votes to become the new president and to make the administration operational.
Caledonia Together has one minister Philippe Germain who abstained in the presidential election, leaving the only anti-independence candidate for the top job, Thierry Santa, one vote short of becoming the president.
The UPM's Victor Tutugoro has told the public broadcaster that he objects to key policies of Mr Santa's side, which wants the restricted electoral roll loosened and which is in favour of further immigration.
The 11 ministers will be convened by the French High Commissioner within two weeks for the next attempt to elect a president and thereby form a functioning government.
Until a new president is elected, Mr Germain, who is the former president, remains in a caretaker roll.