Mr Natuman was elected by 40 of the country's 52 MPs on Thursday after a successful motion of no-confidence to remove Moana Carcasses as prime minister.
Our correspondent says moves are already underway by Mr Carcasses to organise a motion of no-confidence against Mr Natuman.
But Hilaire Bule says Mr Carcasses has only collected 17 signatures so far and needs 27.