This means that from Monday meetings of any size as well as all sports competitions are again allowed.
The wearing of masks on public transport can be discontinued and bars and restaurants no longer need to register patrons.
The president Thierry Santa said there was no local circulation of the virus and that all 21 cases were imported.
One person is still in hospital care.
The border remains closed except for flights from Wallis and Futuna which is the only French-run territory without any Covid-19 case.
Regular air travel will continue to be limited to repatriation flights for stranded residents and for some French personnel.
All arrivals in New Caledonia except from Wallis and Futuna have to isolate for two weeks in designated accommodation and then self-isolate for another week, although Mr Santa suggested the third week was being reviewed.
New Caledonia's international airline is not expected to resume services before August.