The Sea Shepherd organisation in New Caledonia says more sharks have been culled near Noumea.
The provincial government has given no details of its operation but says there is no question of waiting for another accident to happen.
Sea Shepherd said according to its volunteers about half a dozen sharks were killed in the middle of last week.
Environmental organisations said they had not been part of any discussions to proceed with the latest cull.
In May, a boy lost a leg in a shark attack in a Noumea bay, triggering an awareness campaign with the involvement of environmentalists who now say they have been excluded.
Initial conclusions were to advise swimmers against being in the water at dusk and dawn or after heavy rain.
Also in May a fisherman was killed in a shark attack in the far north of New Caledonia.