Air France planes are parked on the tarmac of Charles de Gaulle airport on Sept. 24, 2014 in Roissy during the Air France pilots' strike. Stephane de Sakutin/AFP/Getty Images

In an attempt to end a crippling 11-day pilots’ strike, Air France-KLM said Wednesday night that it would scrap its plans to shift the bulk of its European operations to low-cost carrier Transavia and called on its pilots to return to work immediately. But a representative of the Air France pilots’ union responded that the strike would continue, despite the airline’s concession.

The strike has resulted in the grounding of more than half of the airline’s flights, costing Air France 20 million euros ($25.4 million) a day and stranding hundreds of thousands of passengers.

The Transavia plan is what prompted pilots to walk off the job in the first place: Air France pilots worried that their jobs would be outsourced to countries that can pay their pilots less money. Air France, which has been losing money on short-haul flights for years as discount airlines such as Ryanair and EasyJet capture more of that market, hoped to stem the tide by investing $1.28 billion to expand the discount Transavia unit.

It's unclear why Air France pilots’ union, known as SNPL, rejected the offer Wednesday night. But a representative of SNPL, which represents 71 percent of Air France pilots, said the unions responded with a counteroffer that was rejected by the airline. Another counteroffer is on the table, to be discussed in negotiations that resume Thursday afternoon.

Air France-KLM has some of the highest staff costs of all European carriers, the Financial Times reports. According to Fortune magazine, Air France captains earn 20 percent more than Transavia's and receive generous company pensions. Meanwhile, they spend 630 hours a year flying, compared with 700 hours at Transavia and 800 or more at Ryanair and EasyJet.

If the strike isn't resolved soon, some fear for the existence of the airline itself. “No airline is immortal, and that includes Air France,” Air France-KLM CEO Alexandre de Juniac noted on French television on Monday.