PARIS -- Air France's leading pilots union on Sunday announced an end to a 14-day strike that grounded roughly half of the airline's flights, stranded passengers worldwide and led to stern shows of frustration by the French prime minister.

After a late-night, 15-hour negotiating session with management, leaders of the SNPL pilot union walked away with no accord, but with the realization that the strike "is not an end in itself," said union spokesman Antoine Amar. The union was "taking up its responsibilities" and ending the walkout so that service can now resume and negotiations can continue peaceably, he said.

Air France, in a statement, said that service would "progressively" start returning to normal on Tuesday -- meaning that flights already cancelled between now and then won't be reinstated. The company hailed the end of the strike, saying it "will have been costly and damaging. It has only lasted too long."

Alexandre de Juniac, chairman and CEO of parent company Air France-KLM, said management team members "are aware of the trauma that our customers, employees and partners just lived through," according to the statement.

At the centre of the standoff are Air France's ambitions to develop a low-cost affiliate, Transavia, to tap into new markets in both France and elsewhere in Europe and better compete at a time when budget airlines have cut into the market share once dominated by giant European carriers like Air France.

The pilots union said it didn't oppose those plans to build the new business, but rejected the labour conditions that management had planned. They started the strike two weeks ago out of concerns that management was looking for a way to outsource their jobs to countries with lower taxes and labour costs.

In a tactical retreat, the carrier's management offered Wednesday to scrap a central part of the plan to shift most of its European operations to Transavia. But the pilots remained unsatisfied, saying the contracts sought for the low-cost carrier's operations in France alone were insufficient.

Air France, in its statement, "confirmed its decision to continue its accelerated development of Transavia in France, without delay" -- which suggested that issues remain unresolved. The carrier said it is sticking to plans to create 1,000 jobs in France through Transavia carrier, including 250 pilot positions.

Several would-be passengers interviewed by The Associated Press expressed frustration and anger during the strike; some grumbled about the tendency of many French workers to strike -- and snarl services in the process.

Speaking to reporters Sunday, Prime Minister Manuel Valls said: "This strike was misunderstood, it was corporatist. It was selfish."

"It inconvenienced hundreds of thousands -- millions -- of consumers. It inconvenienced other Air France staffers who made a number of sacrifices over the years. This strike costs a lot in terms of the company's image," he said. "And it has left a trail of division, fracture within its ranks."

Air France-KLM said previously that the walkout was costing up to 20 million euros ($25 million) a day. The French state holds a 16-per cent share of the company, and appoints three board members, a spokeswoman said.

Valls, a Socialist, said the Transavia plan was "indispensable" -- and sought to parlay Air France's woes as a metaphor for France's need for reforms more broadly.

"We are in a competitive universe, the low-cost one, and it needs to be faced with the proper weapons," Valls said. "It shows our country needs reforms at every level, and it's true especially in the transportation sector."