On whether the air traffic controller should compensate airlines, Wallace said: “That is a discussion that should be happening.”
Five flights were held in the air, three of them diverted back to New Zealand.
Wallace said Airways should take steps around “reassuring the industry that everything is up and running and reliable”.
Airways said it had communicated with organisations impacted by the outage.
It said its main oceanic air traffic control system had an outage and operations were switched to a backup system on Saturday.
“The investigation into the source of the error is ongoing,” an Airways spokesperson said.
Airways NZ chief executive James Young told Herald NOW a system issue linked into the transfer of data was to blame.
On compensation for airlines, Young said: “That’s a conversation that we would have to have at some point down the track, but that is not normal.”
A state-owned enterprise, Airways has air traffic service customers including airlines, airports, commercial and private operators, and recreational flyers.
Late last month, it said the average price increase for commercial airlines would be 17.7% across the three-year period to 2028.
That was down from a 22.8% hike proposed earlier in the year.
Massey University School of Aviation chief executive Ashok Poduval said as a pilot he had not encountered a major air traffic control systems failure.
But he added: “I have encountered situations where aircraft have been put in holding patterns due to congestion at the airport.”
He said aircraft had contingency fuel, and pilots would know how long they could stay in holding patterns.
Most air traffic control systems had backup systems that came into effect quickly, he added.
“This is extremely rare, so it must have been something most unusual,” Poduval said of Saturday’s event.
“I’m sure the investigation will reveal what went wrong, and appropriate measures will be put in place.”
The Civil Aviation Authority (CAA) said it would engage with Airways NZ on preliminary findings from a technical review early this week.
The CAA said Airways NZ would conduct a full review of the incident including a “root cause analysis”.
Air New Zealand chief safety and risk officer Nathan McGraw said the airline was in contact with Airways.
He said the airline would review the findings once the investigation was complete.
New Zealand’s oceanic airspace, known as the Auckland Oceanic flight information region, covers an area almost four times the size of Australia.
The region stretches from the Antarctic to 5 degrees South, and across the southwest Pacific.
Australia’s Airservices manages 11% of the world’s airspace, from the Antarctic to 2 degrees South and across the southern Indian Ocean.
John Weekes is a business journalist covering aviation and courts. He has previously covered consumer affairs, crime, politics and courts.