SYDNEY—Airlines resumed some flights to and from a southern Australian city on Monday after an ash cloud from a Chilean volcano forced hundreds of cancellations over the weekend, but most flights to and from New Zealand were still grounded.

Several flights to and from the southeastern Australian city of Melbourne, the state of Tasmania and New Zealand were canceled on Sunday after ash, which can damage engines, moved across the Pacific. In total, more than 55,000 passengers have been stranded by the disruptions, which came amid a three-day holiday weekend in Australia.

The cloud moved away from Melbourne on Monday afternoon, though, and national carrier Qantas and its budget subsidiary Jetstar resumed flights into and out of the city.

It could take 24 to 48 hours to clear just the Melbourne backlog, according to a Qantas spokesman. He spoke on condition of anonymity, citing policy.

Both airlines continued to ground flights to Tasmania and New Zealand, citing the danger ash poses to engines.

Budget carrier Tiger said flights would remain canceled until Monday evening, spokesman Vanessa Regan said. But some airlines have taken to the skies, flying below the cloud.

Air New Zealand, in fact, never suspended service, instead choosing to divert flights and alter altitudes.

Virgin Australia canceled flights on Sunday but started flying out of Melbourne, Tasmania and New Zealand again on Monday morning with a reduced schedule. As the airline struggled to get planes to where they need them, more than two dozen Virgin flights were still suspended on Monday, said company spokesman Melissa Thomson.

Qantas rejected flying below the cloud.

“This is about Qantas safety standards and procedures in place. We want to ensure the safety of crew, the safety of our passengers and ultimately the safety of our airlines,” said Olivia Wirth, a Qantas spokesman. “So until such time that we get greater clarity on the ash cloud and until it removes, we will not operate services.”

New Zealand’s Civil Aviation Authority had some good news for airlines flying below the cloud. It said it was now safe for planes to fly up to 27,000 feet (8,000 meters), up from 20,000 feet (6,000 meters), according to spokesman Bill Sommer.

The plume of ash could disrupt travel for the next several days, according to Airservices Australia. The drifting clouds of fine grit can severely damage airplane engines. The Cordon Caulle Volcano in southern Chile began erupting June 4. Flights in the South American countries of Chile, Argentina, Uruguay and Brazil were grounded for some days following the eruption.

The flight warnings and disruptions come 14 months after air traffic was grounded across Europe after the eruption of Iceland’s Eyjafjallajokull Volcano.