Reports from Wallis say the French government has agreed to only recognise the traditional king, the Lavelua Tomasi Kulimoetoke.
A reporter for the local public broadcaster says this has emerged after this morning's talks which came after yesterday's abandoned attempt by a rival clan to choose a new king.
Wallis has seen days of disruptions triggered by the announcement that a new king would be installed by a clan which has been described as pro-reform and pro-French.
Backers of the Lavelua set up blockades along key roads and damaged and shut down the airport to prevent French reinforcements from being flown in.
A French mediator, Louis Lefranc, arrived from Noumea yesterday in a bid to defuse the tension which on Friday reportedly left one person injured in a clash at a blockade.
New Caledonia's daily paper reports that no police reinforcements were sent on yesterday's military flight because some of the men at the barricades are armed.
The rivalry has left schools closed for days and the island's administrator ordered public servants to stay home.
The crisis deepened in May when the Lavelua challenged the French judicial authorities and asked them to leave the island.
In 1961, the Lavelua signed the agreement that saw Wallis become a French territory.
