Air New Zealand says it will have 97% of passengers back on flights on Tuesday after the grounding of its fleet of 11 ATR planes.
The aircraft, operated by subsidiary Mount Cook Airlines, were inspected by engineers after hairline cracks were discovered near the window of the cockpit of one plane in Christchurch.
The entire fleet was grounded on Sunday and since then about 5000 passengers have been affected.
Air New Zealand says four of the planes are now back in service and one more should be in the air on Tuesday evening.
The airline says three ATR planes have been found to need repair work, which will be completed by Sunday.