The French High Commissioner in New Caledonia, Laurent Prévost, plans to called members of the incoming government for a meeting on Tuesday 2 March to try and elect a new president.
It is the first time in decades that the majority of ministers in the territory's 11 member collegial government are pro-independence Kanaks.
The two pro-independence groupings, UC FLNKS and UNI, have so far been unable to agree on a candidate for president.
An earlier attempt to elect a president saw a split vote with French Loyalist candidate Thierry Santa getting four votes, and Louis Mapou of UNI and Samuel Hnepeune of UC FLNKS getting three votes each.
The single Caledonie Ensemble minister abstained from voting on that occasion.
This is all against a backdrop of intense socioeconomic stress with the pandemic and trouble within the local nickel sector and a government budget needing to be passed by April.