Tropical Cyclone Freda has continued to weaken and is now classified as a depression.
An orange alert is still in force for New Caledonia's Belep islands in the north.
By midday on Tuesday, the system was about 200 kilometres northwest of the territory.
The metservice says at its centre, the cyclone has dropped its sustained wind strength to about 110 kilometres an hour.
It also says there will be heavier rain in the north, being brought by easterly winds gusting up to 100 kilometres an hour.
The storm is forecast to move at about 10 kilometres an hour in a southerly direction before beginning to veer towards the southeast.
This would put Freda on a trajectory parallel to the main island's west coast.
The storm has been in the Coral Sea since the weekend after having brought heavy rain and damaged crops in parts of Solomon Islands.