The French overseas minister, Brigitte Girardin, is reported to have told the President of French Polynesia, Gaston Flosse, that France would "turn off the taps" if the pro-independence leader, Oscar Temaru takes power.
The report in La Depeche de Tahiti comes as France has sent 150 police to the territory this week, with a further 150 due next week.
The opposition Tavini Huiraatira party, led by Mr Temaru, has now formed a majority coalition following last week's election and is poised to form the new government.
A Tavini spokesperson, Tea Hirshon, says they have sent an open letter to Mrs Giradin, asking her to confirm whether the reports are true.
Mrs Hirshon says although it is a concern, they are confident that Mrs Giradin will not go through with her threat.
"We don't believe it will happen because there are laws and we have conventions that have been signed with them and it will not happen. I think it's a scare tactic that they're using to try to destabilise Oscar Temaru and the union majority."
A Tavini spokesperson, Tea Hirshon.
On the eve of the election of a new president of the territorial assembly, Mr Flosse has again said that it was never the people's will to oust his Tahoeraa Huiraatira Party.
He says his party won most votes and the opposition group now being presented in the media is only united in wanting to oust his party.
Mr Flosse says the programmes of the various groups are not compatible and will lead to some MPs betraying their voters.
His latest talks with the pro-autonomy leader, Philip Schyle, failed to give him the one seat to have a majority.
Mr Schyle has told the Tahitipresse news agency that maybe the election of a president, which is due next week, should be brought forward.
Meanwhile, the Socialist Party in France, which signed a co-operation agreement with Tavini before the elections, says it will send a team
to Tahiti in the light of the latest developments.
In a debate in Paris, the party asked her whether she had been calling French Polynesian MPs to avoid Mr Flosse's defeat.
And she warned against preparing a bad coup by sending police to Papeete.