Public services have gradually re-opened this morning in the New Caledonian capital Noumea after the territory was battered by the cyclone.
The cyclone was now a category two storm after hitting the island as a category three and is heading south.
The latest warning advising people to limit their movements during the clear up was lifted at midday local time.
President of the government Philippe Germain praised New Caledonians for taking heed of the warnings which left the territory relatively unscathed.
Four people were reported to have been injured in New Caledonia after the storm crossed the main island overnight.
Authorities said workers had been out clearing fallen trees off roads and ensuring safety since dawn.
The local media reports thousands of people still remain without power, and there is debris from fallen trees and some damage to homes.
Swimming at all Noumea's beaches was banned for 48 hours.
Meteo France said in Thio, on the east coast, a total of 350mm of rain fell in 24 hours and authorities were also recommending people in some areas boil water for consumption and limit their water usage.
Areas included Dumbea, Mont Dore, Paita, La Foa and Boulouparis.
Scheduled Air Calin and Air Caledonie flights in and out of Tontouta have been cancelled today and scheduled flights are set to resume tomorrow.
There are no scheduled Air New Zealand flights to the territory today.
Meteo New Caledonia forecaster Virgil Cavarero told Reuters the category three cyclone had been predicted to hit as a category four, which would have been even more devastating.
Heavy rain, gales and high seas around New Caledonia will gradually ease tomorrow as it moves away.