The French Polynesian government has proposed holding the second round of the delayed municipal elections on 21 June.
Voting was due on 22 March but the spread of Covid-19 prompted Paris to cancel it and on 23 March it declared a State of Emergency.
French Polynesia's president Edouard Fritch unsuccessfully lobbied the French government to let French Polynesians vote, considering the low number of infections to be posing no risk.
While France is yet to fix its date for the second round, French Polynesian mayors would like to have the election on 14 June and the government on 21 June.
Opposition parties said they would like to have all restrictions first lifted to allow for proper campaigning.
In the first round on 15 March, several prominent politicians secured an absolute majority and were elected.
Among them were Mr Fritch and the pro-independence leader Oscar Temaru.
The vice president Teva Rohfritsch tendered his resignation after he fell short in his bid to secure the mayoralty in Punaauia, but Mr Fritch rejected that.
In Papeete, the incumbent Michel Buillard narrowly missed the 50 percent mark to be elected and will have to go to a second round.