He said the new services were "essential" and could see about 25 passengers entering the city a day.
"It is the only air traffic we will have."
Physical distancing precautions would be in place for every flight, he said.
Air New Zealand general manager networks, Scott Carr, said travel remained very restricted under alert level 3.
"We have made some slight adjustments to our domestic schedule in the coming weeks and that includes adding several services a week between Auckland and Napier and Auckland and Tauranga.
"We'll also be adding additional capacity between Christchurch and Dunedin with flights in and out of Dunedin across the week."
• Covid19.govt.nz: The Government's official Covid-19 advisory website
Dumble said there would need to be a bit of thought on what alert level 2 will look like and how they may operate.
"We will definitely see a change, once we reach level 2,"
"Connectivity for our city is so important ... we have always had huge demand for air travel to the region."
ALERT LEVEL 3 FLIGHT SCHEDULE:
Auckland-Christchurch
2x return services Mon-Sat
1x return service Sun
Auckland-Wellington
1x return service Mon-Sun
Auckland-Tauranga
3x return services Tues/Thurs/Fri
Auckland-Napier
3x return services Tues/Thurs/Fri
Wellington-Christchurch
2x return services Mon-Fri
1x return service Sat/Sun
Wellington-Nelson
1x return service Mon-Wed
2x return services Thurs/Fri
Christchurch-Dunedin
1x return service Mon-Sun