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NEW: Qantas says all flights are operating on time

NEW: The backlog of domestic passengers will be cleared by early Tuesday afternoon, the company says

Some 100,000 passengers were affected by the grounding of Qantas flights

Sydney CNN  — 

Australia’s Qantas Airways said Tuesday its flights are back to normal after a government labor board ordered it to end a dispute with its unions that grounded the airline over the weekend.

“Qantas sincerely regrets the impact on customers of industrial action over recent months and looks forward to a rapid recovery and period of stability,” the airline said in a statement.

Most international passengers were accommodated on flights Monday and overnight, while the backlog of domestic passengers is expected to be cleared by early Tuesday afternoon, said Qantas, which resumed flights on Monday.

The first planes to depart were an international flight from Sydney to Jakarta and a domestic route from Melbourne to Sydney.

Some 100,000 passengers were affected by the groundings, said Kira Reed, an airline representative.

Labor relations tribunal Fair Work Australia ordered an end to the labor dispute “to avoid significant damage to the tourism industry” after Qantas grounded its jets Saturday afternoon.

The airline grounded 447 flights and, ahead of the order to end the dispute, had announced it would lock out its unionized pilots; engineers; and ramp, baggage and catering crews effective Monday evening.

The dispute with the unions has dragged on for 14 months, the labor board said.

Qantas argued that the unions’ demands would leave the airline “seriously impaired or destroyed.” The labor board gave the two sides three weeks to reach an agreement, with a possible three-week extension if talks were making progress.

The labor board gave the two sides three weeks to reach an agreement, with a possible three-week extension if talks were making progress.

The decision “provides certainty for Qantas passengers,” Joyce said in a statement following the decision. He apologized to passengers and said flights would resume as early as Monday afternoon.

The Australian and International Pilots Association said it hoped for a “positive outcome” from the talks, calling the decision to ground the airline a “gross overreaction” to its demands. “It is a sign that the current management has lost touch with the traveling public, its workers and the basic Australian ethos of free speech,” the union said in a statement.

The labor dispute involves three unions representing air and ground staff of Australia’s largest domestic and international airline.

Union officials have accused Qantas of planning to outsource ground jobs at a cost of thousands of Australian jobs and of putting profits first. Pay and working conditions have also been at the center of the dispute.

Qantas, which has its headquarters in Sydney, is the second-oldest airline in the world, and marked its 90th anniversary last year.

It employs about 32,500 people and flies to more than 180 destinations worldwide, according to the company website. For the financial year ending June 2010, it made a post-tax profit of 116 million Australian dollars.

CNN’s Hugh Williams and Pamela Boykoff contributed to this report.