After five days of disruptions, media reports say a deal has been reached between the authorities and publicly employed firefighters.
An agreement is yet to be concluded with all firefighters on the payroll of the private company running some of the dozens of airports across the archipelago.
Only a couple of islands had maintained links with Tahiti, throwing travel plans of several thousand people into disarray.
The stoppage also imperiled medical evacuations.
The partial settlement clears the way for a gradual resumption of services to the outer islands.