Elbers' 4-year term expires in April, and Air France's board is due to meet in Paris on Feb. 19 to discuss strategy ahead of earnings on Feb. 20.

New CEO Ben Smith has pushed for deeper integration among the airline's operating divisions since his appointment last autumn. KLM has fiercely guarded its structure and brand since its acquisition in 2003, leading to tensions between Elbers and Smith.

The petition was signed 25,000 times by KLM employees, out of 35,000 total, in a strong display of support for Elbers. Signatories credited him with the airline's success and said they were afraid of the consequences if he is dismissed.

"There would be a very real risk of unrest among the employees and unclear and potentially unstable management if Pieter Elbers were to be forced to step down," a letter accompanying the petition and addressed to Air France chairwoman Anne-Marie Couderc said.

The relative outperformance of the Dutch subsidiary under Elbers has also caused tensions within the group. Air France was hit by repeated costly strikes, even as KLM staff weathered successive rounds of cost-cutting and layoffs.

For the first 9 months of 2018, Air France Group reported operating profit of 328 million euros ($370 million), while KLM had operating profit of 960 million euros.

Dutch Finance Minister Wopke Hoekstra has also voiced support for Elbers, and met his French counterpart Bruno le Maire on Monday to discuss the situation at Air France-KLM.

The French government holds a 14.29 percent stake in the group.

(Reporting by Toby Sterling. Additional reporting by Laurence Frost; editing by David Evans)