Talks between Air France and its pilots reached an impasse on Saturday after a union request for a mediator was rejected by both the airline's management and the French government.
Air France has been locked in negotiations with pilots over plans to create a low-cost operation, resulting in a 13-day strike which has cost it up to 20 million euros ($25 million) a day.
The company said on Saturday it would only be able to operate 45 percent of its flights on Sunday, fewer even than on Saturday, as more than half of its pilots would be on strike.
French Prime Minister Manuel Valls and Air France rejected pilot unions' demands that an independent mediator was appointed.
“Management does not think that the appointment of a mediator is necessary,” Eric Schramm, co-head of operations at Air France, told BFM TV on Saturday.
The pilot union SNPL had said on Friday it stood ready to lift the strike as soon as a mediator was appointed.
Pilots are trying to pressure Air France to offer the same contracts to those flying on the proposed new Transavia unit as to its own pilots, a demand the airline argues is incompatible with the low-cost model it seeks to exploit.
French Prime Minister Valls put pressure on the pilots on Friday, calling for them to accept the deal put forward by the airline to end the conflict.
“This strike must end,” Valls said. “This strike is intolerable for customers, this strike is intolerable for the company, Air France, this strike is intolerable for the country's economy.”
The government is a 16 percent shareholder in the group and sits on the board.