There is a call for France to extend its state of emergency in force since last year's Paris bombings to French Polynesia to counter Islamic radicalism.
Lana Tetuanui, who is one of the territory's members of the French Senate, made the call after news broke that three prisoners at the Nuutania jail have been registered as Islamic radicals and a risk to safety.
One of the three was in court this week for assaulting corrections personnel and according to police accounts, he spoke of his desire to commit extreme acts against anyone who was not a jihadist.
Reportedly, he approved of the attack in Nice in July.
Mrs Tetanui said urgent action had to be taken to curb the spread of radicalism as it no longer holds true that Tahiti's isolation is its protection.
The French High Commissioner Rene Bidal said he had been advised of the development at the prison after saying in July that nobody in French Polynesia was classified as a security risk.
The president issued a statement warning against giving in to a psychosis.
He said at this stage one had to be reasonable, pointing out that those identified as radicals were in jail.
Should they be released, he said, they would no doubt be placed under surveillance.
Earlier this week, reports from France said a 20-year-old French Polynesian man had been heard in court amid suspicion he was affiliated to Muslim extremists and wanted to blow himself up in Paris.
French media said under emergency laws the man was heard behind closed doors in Besancon to secure authorisation for access to his computer.
The man was released but investigations continue.