Teams are working around the clock to fix the pipeline after damage from a digger caused it to burst on September 14, operator Refinery New Zealand said.
"The pipeline should return to service between September 24 and 26," it added.
Air New Zealand said fuel supplies at the airport were down to 30 per cent of normal capacity, forcing some long-haul flights to make additional refuelling stops at airports in Australia and the Pacific, the BBC reported.
The carrier said about 2,000 passengers were affected by cancellations on Monday.
At least 27 international and domestic flights were cancelled over the weekend.
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