Air NZ's Captain David Morgan said on Monday evening flights would only resume when they were assured of the security of the airport and safe access for passengers and staff.
Later, the airline said its "next scheduled service is Saturday 25 May, however, we will continue to review this and may add capacity when the airport reopens".
AirCalin said on Monday night the Nouméa airport would be closed until 23 May.
The capital descended into chaos last Monday, after riots protesting a new law that would allow French residents who have lived there for more than 10 years to vote - which some say will weaken the indigenous Kanak vote.
Six people have been killed, and more than 230 people have been arrested. A state of emergency was declared on Wednesday, and about 1000 French police and military officers arrived to end the riots.
The rioting started over the French National Assembly’s vote to allow French residents who have lived in New Caledonia for more than 10 years to vote.
A New Zealand Defence Force Hercules is on standby to bring 250 Kiwis home, but it is awaiting clearance from French authorities.
Hundreds of armed French police have been using tanks to clear protesters and roadblocks between the international airport and Nouméa.
The dangerous route - which stretches for about 50 kilometres north of the capital - is the key reason why the airport remains closed.
Shula Guse from Canterbury, who was on holiday with her partner and friends, said many shops are running low on stock.
"The shops are closed or if they're open they have empty shelves, the local corner dairy has nothing on the shelves," she said.
Guse said she managed to buy some flour and yeast from a local pizza shop and had started making her own bread.
She said her group had their flights rebooked for Tuesday - but there had been no confirmation from Air New Zealand on whether it will go ahead.
Guse, whose friends are running low on heart medication, said they would have to make other plans if the flights fell through.
"When (Monday) is finished, and we haven't heard any news, then we might start ... looking for more medication, more food, just to make sure we have enough."
"We've set up a sense of a roster, or a shift, that watches over the night time for the university, and this high-strung suspicion from every noise, every bang, that is that someone coming to the university," she said.
Roylands said she was not sure if the French police would be able to successfully clear the main road to the airport.
"Clearing the road for an hour north seems like an impossible task with these rioters," she said.
The Ministry for Foreign Affairs and Trade (MFAT) said the NZDF Hercules was ready to go as soon as French authorities gave permission.
When asked whether the navy would be deployed, MFAT said its focus is on flight repatriation.
When RNZ asked whether New Zealand would consider helping to evacuate people from other Pacific countries who were stranded in New Caledonia, MFAT said it had been engaging with Pacific partners about the situation.
Foreign Minister Winston Peters said he was unable to put a timeframe on how soon New Zealanders would return.
He said they are continuing to explore possible options, which included working alongside Australia and other partners to help get New Zealanders home.
