The flight had already been delayed almost 12 hours due to the ash.
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Another Air New Zealand return service was scheduled to depart Denpasar at 4.30pm today and arrive in Auckland at 4.35am tomorrow, the spokeswoman said.
The spokeswoman said about 200 passengers were originally scheduled to travel from Denpasar to Auckland at the weekend. But she said they were not all Kiwis.
"This number will also include customers who are based in Bali or elsewhere."
The two flights were the only scheduled services between Auckland and Bali today.
A Jetstar flight to Bali is also scheduled to leave Auckland at 2.20pm.
Jetstar resumed services on Monday, flying stranded passengers out of Bali as the safety threat from the volcanic ash cloud died down.
About 40 flights in and out of Bali were expected today if conditions remained clear.
Jetstar chief executive David Hall told ABC Australia two 300-seat planes would be sent to Bali today.
"It's a day-by-day proposition but as soon as the skies are clear, we're mobilising as much capacity as we can to get customers home," he said.
The Ministry of Foreign Affairs and Trade is advising Kiwis with Indonesia travel plans to confirm their travel arrangements with their airline or travel agent directly, prior to heading to the airport.
There are 440 New Zealanders currently registered with Mfat as being in Indonesia.
Travellers should register their details on www.safetravel.govt.nz and ensure they have a comprehensive travel insurance policy in place, an Mfat spokesman said.
Insurance Council New Zealand's communications manager Sarah Knox said travel insurance cover in this situation was dependent on each provider.
"Call your travel insurance company to discuss your situation, as all insurers have 24-hour assistance available."