The New Caledonian president, Philippe Gomes, says if the pro-independence Caledonian Union pulls out of the collegial government, there will have to be fresh elections for the three provincial assemblies.
Mr Gomes has told the Nouvelles Caledoniennes newspaper that the party's threat to resign amounts to a coup attempt by the Caledonian Union and the Rassemblement-UMP.
The pro-independence camp has been meeting since last night to discuss a possible withdrawal from the executive.
Mr Gomes says under the provisions of the 1998 Noumea Accord, government institutions need to work in a consensual manner.
He says a departure by one group automatically means the end of the collegial government which is made up in proportion to the parties' relative strength in the territorial Congress.
A key point of contention is the choice of flag, with Mr Gomes advocating a new flag to express the territory's identity.
Since last year, the French tricolore and the Kanaky flag are used jointly on many public buildings.
Paris says it is following closely the New Caledonian discussions.