The French High Commissioner in New Caledonia, Vincent Bouvier, has convened a government meeting on Thursday in a fresh bid to get it to elect a president.
The territory has been without a president for five weeks after one of the three anti-independence parties quit the collegial government and triggered its collapse.
The government represented three anti-independence parties, which jointly had six of the 11 ministries.
On New Year's Eve, the Congress re-elected the same government, which then however failed to agree on a president.
Cynthia Ligeard has continued as caretaker president, saying the territory's administration remains assured.
However, the High Commissioner says it is a necessity for the territory to have a proper government, echoing the French overseas minister's concern at the deadlock.
Mr Bouvier has held talks with local politicians, who have shown no sign to compromise.
The deadlock could be broken if the five pro-independence ministers ended their abstention and backed either Mrs Ligeard or her rival, Philippe Germain.