The union representing Air Canada flight attendants says it will continue to defy a back-to-work order despite the Canada Industrial Relations Board ruling their strike "unlawful".

The independent federal tribunal deemed the job action by the cabin crews - now in its third day - illegal on Monday after the union defied a government back-to-work order issued over the weekend.

"If Air Canada thinks planes will be flying this afternoon, they're sorely mistaken," said Canadian Union of Public Employees president Mark Hancock.

The strike by more than 10,000 flight attendants for Canada's largest airline has stranded tens of thousands of passengers since flights were grounded on Saturday.

Air Canada has not yet responded to the union's latest move.

The airline said earlier that it planned to resume flights by Monday evening, but a notice on its website as of Monday afternoon said its operations "remain suspended".

It added that all flights by Air Canada and Air Canada Rouge were cancelled until 16:00 EDT (21:00 BDT) on Tuesday.

The trade organisation that represents Air Canada and other major Canadian firms, such as WestJet and FedEx Canada, condemned the union for defying the order, saying they "are normalising the idea that if you don't like a decision, you can simply ignore it".

"That is not labour relations, it's a reckless path that erodes trust in the labour relations system, weakens our global reputation, and undermines economic stability at a moment of heightened geopolitical uncertainty," said Daniel Safayeni, president and CEO of Federally Regulated Employers - Transportation and Communications (Fetco), in a statement.

The Canada Industrial Relations Board decision ordered the union to send its members back to work by 12:00 EST (16:00GMT) on Monday, and also directed the members to return to their duties.

It is unclear what consequences the CUPE now faces for its defiance.

At a news conference, Mr Hancock said the union is willing to accept any penalties for its refusal to comply, including monetary fines and jail time.

"If it means folks like me going to jail, then so be it," he told reporters, adding that the union will only accept to resolution through a negotiated settlement at the bargaining table.

Under Canadian law, the union and individual workers could be fined or sanctioned for refusing to return to work, Western University law professor Michael Lynk told Reuters.

Prime Minister Mark Carney said it was "disappointing" that Air Canada and its cabin crew were unable to reach an agreement after eight months of negotiations.

"We are in a situation where literally hundreds of thousands of Canadians and visitors to our country are being disrupted by this action," Carney said in Ottawa on Monday.

"I urge both parties to resolve this as quickly as possible."

The airline estimates some 500,000 passengers have so far been affected by flight cancellations.

Stranded passenger Jenny Phelps told Reuters she struggled to reach the airline while trying to rebook her cancelled flights.

She said that, while she supports the strike action by the flight crews, she's on the hook for three extra hotel nights and called the experience "super stressful and very expensive".

In their remarks on Monday, union representatives apologised for the impact the job action has had on travellers across Canada.

"Our fight is not with you. We do not want to be here," said Candace Rennick, the union's national secretary-treasurer.

"But these workers, who are mostly women, have waited too long to have their issues addressed."

Flight attendants are calling for higher salaries and to be paid for work when aircraft are on the ground.

In contract negotiations, Air Canada said it had offered flight attendants a 38% increase in total compensation over four years, with a 25% raise in the first year.

CUPE said the offer was "below inflation, below market value, below minimum wage" and would still leave flight attendants unpaid for some hours of work, including boarding and waiting at airports ahead of flights.

The union and the airline have publicly traded barbs about each other's willingness to reach an agreement.

On Saturday, Jobs Minister Patty Hajdu ordered binding arbitration to end the dispute.

CUPE made the rare move of directing its members to ignore a back-to-work order on Sunday and accused the government of "caving to corporate pressure".

Earlier this month, 99.7% of employees represented by the union voted for a strike.