The anti-independence Caledonia Together party has criticised rivals within the anti-independence camp for helping elect a vice-president last week.
The 11-member collegial government elected the pro-independence candidate Gilbert Tyuienon after the Future with Confidence ministers broke the stalemate.
A week earlier, they had abstained along with Caledonia Together's only minister which meant Mr Tyuienon could not secure a majority.
Future with Confidence has 5 of the 11 ministers and they voted for Mr Tyuienon to give him the minimum six votes needed.
In a statement, Caledonia Together says by now voting for Mr Tyuienon, a political goal was pursued and that was to restore a coalition with the pro-independence Caledonian Union.
It also says it took no time for Future with Confidence to renounce its election campaign promises and form a alliance which goes against nature.
The party says there was no legal basis forcing the election of a vice-president.