Bruno Le Maire's warning that Air France could "disappear" comes as staff begin another round of industrial action over a pay dispute.
Before that, the President of Air France and CEO of Air France-KLM, Jean-Marc Janaillac, resigned, as he had promised in the case his proposal did not obtain the support of the workers.
The company had offered a staggered 7 per cent pay increase over four years, with 2 per cent in 2018 and further increases dependent on the airline's financial performance.
The Air France-KLM board asked Mr Janaillac to stay on until May 15 when it will put a transitional leadership in place.
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Despite the French state owning 14.3% of the Air France-KLM parent group, the loss-making airline would not be bailed out, he said.
Air France reported Friday that it lost $320 million in the first quarter of 2018, adding that the strike will lead to at least $330 million more in lost revenue through the end of the year.
Air France's share price plunged almost 13% at the open on Monday and was trading 10.9% lower at 7.21 euros in the early afternoon in Paris amid questions about its future management and direction.
It was estimated that about 14 percent of Air France pilots, about 18 percent of flight crews and 10 percent of ground staff would participate in a strike on Monday. On medium-haul flights to and from Paris-Charles de Gaulle, the percentage drops to 80%, while it expects to operate 87% of short-haul flights to and from Paris-Orly and the rest of the regional airports.
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After negotiations reached deadlock, Janaillac called a vote last Friday, the results of which went against him.
But many analysts say Air France has lagged far behind in restructuring and has failed to address its continued losses.
A May 4 electronic vote resulted in a "no" vote to the plan by a majority of Air France staff.
Staff and management at the carrier have been locked in a dispute over pay since February.
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Air France said on Friday that 13 days of strikes by its staff had already cost it about €300 million ($358 million). The agreement, rejected by the trade unions, outlined a 7-percent salary raise between 2018-2021, with a 1-percent salary increase in 2018.