Wallace said refunds were currently costing the airline $22 million a day.
The national carrier has already ditched 4000 jobs, and some employees have taken a 30 per cent pay cut.
The company has had more than $70 million from the government wage subsidy scheme but said it would need to rely on the second round of subsidies for millions more.
Last April it carried 1.4 million passengers. This April the number was just 15,000.
Chief executive Greg Foran told RNZ's Checkpoint last week all areas of staffing were up for review, including airport staff, cabin crew, pilots, engineering, maintenance, and home office.
"We burn through cash at about five million [dollars] a day at the moment.
"Our cash when we began dealing with Covid-19 was sitting at about $1.1 billion. We announced to the market a couple of weeks ago that that was now down to $650 million or so. So you can see that we've been through the best part of $500 million through the back end of February, March and April and some of May.
"So you can assume the government loan that we're able to secure, we'll need to access that some time in the next few months.
"If international borders don't open for some time - putting Australia and the Pacific Islands aside - we will have to consider what other options do we take.
The company would definitely have to dip into the government loan of $900 million before the end of 2020, he said.
"Some time in the next few months we'll begin to access that loan and part of the action that we're taking at the moment, whether it be in terms of finding another $150 million, plus some more capital, plus or more [operating expenditure], the way we're dealing with customer credits at the moment.
"This is all about us creating a platform that ensures that this airline gets through this."
Air New Zealand would "certainly" be claiming the next round of the government's wage subsidy, he said.
"I think for Air New Zealand that is about $37 million. We got $79 million in the first round."
Air New Zealand has expressed concerns that it simply does not have enough money available to refund all the customers currently requesting their money back.
- With RNZ