French Polynesia's anti-independence Tahoeraa Huiraatira Party says it wants France to cede its rights to the exploration of the territory's seabed believed to be rich in rare earths.
The call was made by the assembly president Marcel Tuihani in an interview with local television.
This follows a long-standing demand by the pro-independence opposition Tavini Huiraatira that Paris change the 2004 organic law to give French Polynesia access to seabed minerals in its economic zone.
The Tavini has already raised its aspirations with the UN which two years ago reinscribed French Polynesia on its list of territories to be decolonised.
A senior Tavini politician, Richard Tuheiava, has said he wants to prevent a repeat of French moves of 40 years ago when the public was also kept in the dark and two atolls were excised to be turned into nuclear weapon test sites.
Rare earths are believed to be found off the Tuamotu and Marquesas atolls.
French Polynesia's EEZ is now more than 4.7 million square kilometres and accounts for almost half of the water surface under French jurisdiction.
Two years ago, the French Economic, Social and Environmental Council urged the government to secure resources in the seabed off France's overseas territories.
It said France would be negligent not to profit from this as French Polynesia has rare earths, whose reserves are held by China in a near monopoly.
France strongly objects to the UN decolonisation move.