Air New Zealand says 97% of passengers booked to travel with its subsidiary Mount Cook airlines on Tuesday, should be able to fly.
Travel plans of about 2000 domestic passengers were disrupted on Monday after Air New Zealand grounded some of its planes at the weekend.
The planes, operated by subsidiary Mount Cook Airlines, are being inspected after hairline cracks were discovered near the window of the cockpit of one plane during a routine check in Christchurch.
The fleet of 11 ATR72-500 aircraft was grounded on Sunday, affecting 3000 passengers.
Five ATR aircraft will be flying by the end of Tuesday, with two more expected back in service by Thursday.
Mount Cook Airline says it will also use other Air New Zealand aircraft for some flights, but there may be some timetable changes.
It says three ATR aircraft need repair work, which will be complete by Sunday.
A large whiteboard in front of the check-in area at Wellington Airport shows six flights are cancelled from the capital on Monday.
They are NZ5 flights operated by Mount Cook Airlines to Christchurch, Queenstown, Dunedin and Hamilton. They have been rescheduled and include road travel by bus.
Other major airports including Dunedin, Christchurch and Auckland are also having to re-route some flights cancelled because of the groundings.
The Civil Aviation Authority says Air New Zealand followed the correct procedure by grounding the fleet and it will monitor results of the inspections.