The pipeline operator, Refining NZ, said repairs would take at least a week, possibly two, raising the prospect of ongoing major disruption.
Air New Zealand said 2,000 passengers were affected by flight cancellations on Monday alone as it attempted to minimise fuel usage.
It said the leak meant fuel supplies at Auckland airport were down to 30 percent of normal capacity and some long-haul flights were having to make additional refuelling stops in Brisbane and Fiji.
"Aviation is a critical transport industry and the lifeblood for tourism. We are naturally extremely disappointed with this infrastructure failure," the airline said.
Refining NZ said it believed the pipeline from its refinery to the airport was accidentally damaged by a digger and a 30-strong team was working around the clock to fix the pipe.
But the danger posed by spilled fuel was slowing progress.
"We need to be absolutely clear that it is safe to work in before we can start welding in the new section of pipe," it said.
Deputy Prime Minister Paula Bennett said it was not the government's fault that such an important piece of infrastructure had been left so vulnerable.
"It's a private company that owns it and you would expect them to have better contingency plans," she told Radio New Zealand.
"(It's) a very rare occurrence, it hasn’t happened for 30 years and we don't expect it to happen again."
