French Polynesia's opposition Tahoeraa Huiraatira Party says Oscar Temaru's candidacy for the presidency may end its arrangement with his Union For Democracy.
The party issued a statement a day after the two main opposition parties were joined by Jean-Christophe Bouissou's Rautahi Party, which quit the ruling To Tatou Aia coalition, in a fresh bid to oust the government of President Gaston Tong Sang.
The statement says Mr Temaru's announcement goes against last year's deal with the Tahoeraa which entitles it to provide the president.
Under the statute introduced by France in 2007, a no confidence motion in Tahiti must contain the name of the new proposed president.
The Tahoeraa will meet to formulate its position in view of Mr Temaru's move.
Should the party still approve the motion and the assembly then pass it, it would give French Polynesia its fourth government in a year.
Last February, an early general election was held under a new electoral system in a bid to increase political stability.