Sydney, Australia (CNN) -- Ash clouds from a Chilean volcano prompted numerous flight cancellations in Australia and New Zealand on Sunday, leaving thousands of passengers stranded.

Chile's Puyehue-Cordon Caulle volcano erupted last week.

The Australian Volcanic Ash Advisory Center issued briefings to the aviation industry to allow them to make decisions on safe air routes.

Australia's national carrier Qantas has canceled all flights to and from New Zealand, as well as the Australian state of Tasmania.

Qantas also announced that all Sunday night flights to and from Melbourne have also been canceled.

In addition, Qantas's affiliate Jetstar has canceled more than 60 flights, leaving thousands of travelers stranded in airports in both countries.

Read more on the grounding of flights

Qantas issued a statement saying it will continue to monitor the movement of the ash cloud and its impact on operations.

Virgin Australia said it would cancel two flights to New Zealand on Sunday, but would accommodate passengers in hotels, and will try to book them on flights Monday.

How do airlines assess the hazard?

Air New Zealand took a different approach, saying it does not expect delays or cancellations, and will adjust flight routes and altitudes as required.

"The ash has traveled a great distance at high altitude and remains present at distinct altitude bands between 20,000-35,000 feet," said Capt. David Morgan, a general manager at Air New Zealand.

"As a result, where required aircraft will fly at a lower altitude of 18,000 feet to remain below the ash or operate a slightly different course to remain clear of it."

In 1982, a British Airways 747 Jumbo suffered severe damage, and had all four engines fail when it encountered ash from an Indonesian volcano.

The plane was able to restart some engines before making an emergency landing in Jakarta.

The U.S. Geological Survey says more than 80 commercial aircraft have unexpectedly encountered volcanic ash in flight and at airports in the past 15 years.

Ash ingested by jet engines may lead to the deterioration in performance and engine failure, the U.S. agency says.