The newly-elected 11-member government is due to meet today and to be chaired by the caretaker president, Cynthia Ligeard, who was one of the two unsuccessful candidates in last week's first attempt to choose a president.
The territory's public broadcaster says in view of the continued deadlock, the French High Commission won't organise an election, which means that the administration will remain in caretaker mode and lack the power to launch new policies.
It also says several weeks or even months could pass before Paris declares an official deadlock of the institutions.
The Ligeard-led government fell last month when the Caledonia Together Party quit the ruling coalition after accusing its partners of violating the formal power-sharing agreement drawn up following last May's general election.
The pro-independence minority in the collegial government said last week it would this time vote for one of the candidates of the rival anti-independence side to end the impasse.
The Caledonia Together leader, Philippe Gomes, says if no solution is found within two months, there should be a fresh general election.