French Polynesia's Tahoeraa Huiraatira Party has warned that the ruling coalition it is part of will end if the assembly president's post is not given to it.
The warning was issued by the party's deputy leader, Edouard Fritch, two weeks before the assembly is due to elect its new president.
Mr Fritch says agreements within the coalition must be honoured.
The assembly presidency is reportedly being coveted by the Tahoeraa leader, Gaston Flosse, which has prompted the current assembly president, Philip Schyle, to say that Mr Flosse's' election would be detrimental to the territory's image.
Mr Flosse has been convicted for corruption and been declared ineligible for an elected office, but his lawyers have appealed the verdict in Paris.
The current coalition with the To Tatou Aia group of Gaston Tong Sang was formed last November when he became the fourth president since the early general election in 2008.
The opposition, led by Oscar Temaru, planned to oust the government by January but failed to have the numbers as some members quit its side.