It said it would be able to fly below the ash level to and from Christchurch, Dunedin and Invercargill airports, though Queenstown remained affected.
Chief pilot David Morgan said there would be some delays as flights got back on schedule.
Air NZ estimated about 3800 passengers were unable to fly because of the ash.
Pacific Blue, Qantas and Jetstar were still not yet flying.
Jetstar said domestic and international flights were cancelled for the rest of the day.
"We continue to closely monitor the situation and a decision will be made on long haul international services between Singapore and Auckland later today," the airline said in a statement.
Its call centre was being overwhelmed with people asking about flights, and it asked for patience as it dealt with all the calls.
An announcement on tomorrow's flights was due this afternoon.
Jetstar said its Australian domestic services were expected to run to schedule today and it would put on extra flights to address the backlog.
Air NZ cancelled all morning flights in and out of Invercargill, Dunedin and Christchurch as the ash cloud from the eruption of Chilean volcano Puyehue-Cordon Caulle -- travelling right around the southern hemisphere -- continued to frustrate fliers.
Civil Aviation Authority meteorologist Peter Lechner told Radio New Zealand this morning the main ash cloud was at 8300m above the country but southerly front moving up the South Island moved some of it lower to about 3000m.
"This current small ash cloud is just a finger moving in from a larger body that is to the southwest of the South Island."
Flights around the Southern Alps needed a large, clear block of air to fly safely and as the cloud was down to 3000m it meant there was not enough space for the larger aircraft, he said.
Yesterday evening 11 Air NZ flights were cancelled to and from Invercargill, Dunedin and Christchurch.
Until yesterday Air New Zealand had been continuing to fly all trans-Tasman routes and also domestic routes at a lower altitude to avoid the ash cloud.
The airline was flying well below the ash cloud at the cost of burning 10 percent more fuel.
Jetstar said in a statement it would not be flying into airspace affected by the ash cloud until it was confident it was safe to do so.
"The safety of our passengers, our people and our operations is always Jetstar's No 1 priority."
Affected passengers had the options of deferring travel, arranging to fly in to or out of unaffected airports, or getting a full refund.
