New Caledonia's Front for Unity has ruled out supporting the rival anti-independence Caledonia Together's bid to get the presidency.
The territory has been without a leader since mid-December when the Caledonia Together ministers resigned and thereby prompted the automatic collapse of the government led by Cynthia Ligeard.
The move ended a tri-partite powersharing agreement six months into the government's five-year term, with Caledonia Together claiming her position.
On New Year's Eve, the Congress re-elected the same 11-member collegial government whose members however failed to agree on who should be the president.
Neither Mrs Ligeard of the Front for Unity nor Philippe Germain of the Caledonia Together Party managed to secure the six votes needed to be elected.
Her party says it was the Caledonia Together which triggered the current situation and it is up to it to untangle the situation.
It says it won't accede to the Caledonia Together request that it be given the presidency, adding that the re-elected administration can run routine and urgent matters even in its caretaker capacity.
The party also says the French High Commission can help draw up the 2016 budget.
It says it doubts Paris wants to dissolve Congress and hold fresh elections.
A planned fresh presidential election earlier this week was called off in view of the impasse.