The French Polynesian Intervention Group, or GIP, has ignored a deadline set by the president to end its blockade of the territory's main port in the capital, Papeete.
The leader of the group action, Rere Puputauki, has let fuel tankers through the barricade to allow the resupply of planes, ambulances and fire engines.
The news agency Tahitipresse reports no official negotiations have taken place.
President Oscar Temaru made a televised address on Thursday night giving GIP members 24 hours to return to their duties.
The Tahoeraa Huiraatira opposition party of former president Gaston Flosse has released a statement saying Mr Temaru 'wants conflict'.
It says the incident is a smokescreen to divert people's attention from what it calls the worsening state of the territory's economy.