The leader of the Caledonia Together Party has pitched for his party to take more control of the new territorial government after last week's government collapse.
The government fell after the party of Philippe Gomes resigned from the collegial administration only six months into a five-year term, thereby ending a power-sharing agreement within the anti-independence camp.
Mr Gomes, who has returned from Paris where he represents the territory in the French National Assembly, says the agreement was only possible in the first place because his party, as the biggest one, was prepared to accommodate the rival pro-French groups.
Speaking on local radio in Noumea, Mr Gomes says there is no point in maintaining an illusion of unity, blaming the Front for Unity and the Union for Caledonia within France for the government's collapse.
The outgoing president, Cynthia Ligeard, has blamed Mr Gomes for the collapse, accusing him of having dreams of an absolute monarch.
The parties have until Thursday evening to draw up a list of candidates for a new 11-member government which the Congress is due to elect next week.
The pro-independence parties have decided to present a single list.
Mr Gomes says if the anti-independence camp cannot agree, there should be a fresh election.