The French minister in charge of overseas territories, Brigitte Girardin, has left New Caledonia at the end of a three-day visit which included a review of the 1998 Noumea Accord on greater autonomy.
Mrs Girardin says views among the signatories of the accord have been brought closer together despite the boycott of the talks in Kone by the biggest Kanak party, the Caledonian Union.
She did not elaborate how things have been advanced but said it is never good to refuse a dialogue.
The Caledonian Union has accused the anti-independence RPCR Party of derailing the accord while it alleges that France has failed to guarantee the legality of the accord.
France has not changed the constitution as Kanaks were promised five years ago.
They have been seeking a freeze of the electorate to prevent immigrants from France becoming a majority ahead of future key votes on New Caledonia's status.