The group calling itself the Polynesian Kingdom of Atooi called a news conference near Papeete, saying it is led by its self-styled king Aleka Aipoalani.
It claims to have worked on its new government for three years, it has its own flag and purports to have its own money.
One of the group members told local journalists that they plan to take their cause to the United Nations.
The group said French Polynesia's woes today are due to the French constitution.
Two years ago, another self-styled king in Tahiti, Teiri Athanase, was given a jail sentence for circulating a fake currency of his Pakumotu republic.