The first batch of jet fuel is flowing through the repaired Marsden Point pipeline and is due to reach Auckland Airport by Tuesday.
Energy and Resources Minister Judith Collins said the new section of pipeline has been welded, certified and pressurised, but the fuel will need about 30 hours to settle once it reaches the Wiri terminal in South Auckland.
"It is expected to be ready to load on planes from the early hours of Tuesday morning," she said.
"While great progress has been made on restoring supply through the pipeline, government and industry are continuing to work tirelessly to ensure fuel is still getting where it needs to be."
Three trucks are going between Marsden Point and Auckland Airport twice daily, with five trucks expected on the road on Monday, Ms Collins said.
More than 140,000 litres of jet fuel was trucked to Auckland Airport on Saturday, with 151,000 litres expected to arrive on Sunday.
"The number of flight cancellations has been steadily decreasing, with no domestic flight cancellations this weekend, only five fuel-related cancellations to international flights yesterday, and two expected today," Ms Collins said.