Bruno Le Maire's notice that Air France could "vanish" comes as staff starts another round of new activity over a compensation question.
The survival of strike-hit Air France is to be decided, as indicated by the nation's economy serve.
Air France-KLM boss Jean-Marc Janaillac announced his resignation Friday after staff at the carrier's French operations rejected a pay deal aimed at ending months of walkouts.
Since the 2004 merger with the Dutch KLM carrier, Air France has been unable to return to profitability.
The government said the French state, the largest shareholder with a 14 percent stake, will not bail out the airline.
Monday's walk-out is the 14th day of action. While nearly all long-haul flights are predicted to operate, one in five medium-haul services from Charles de Gaulle airport in Paris won't, with short-haul trips from Orly also affected.
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Both organizations have experienced decreased membership in recent years, the Associated Press reports. Some say that declining BSA membership among young men has helped spur the change in membership policy.
Bank of America reaffirmed a "sell" rating on shares of Air France-KLM in a research note on Monday, February 12th. There have also been strikes at the state-owned SNCF rail company.
Air France-KLM reported a net loss of €269 million ($321 million) in the first quarter of the year.
British Airways and Lufthansa have already undergone heavy cost-cutting in recent years, amid rising competition from low-priced airlines and carriers from the Gulf states.
Travellers should expect last minute delays and cancellations, Air France said, adding it will update its flight schedule for Tuesday later today.
The group has already downgraded expectations of its financial performance for 2018. The joint company flies tens of millions of passengers around the world every year.