If no deal is reached Alitalia could go into liquidation next week
Alitalia will cut 3,000 jobs under a new agreement reached with Italy's four main union organisations, Labour Minister Maurizio Sacconi has said.
"The job cuts... they're around 3,000," Mr Sacconi told an Italian television programme on Monday.
The four unions have signed a deal with CAI, a consortium prepared to invest in a new national Italian airline, but five other unions oppose the deal.
Those opposed to the deal include pilots and cabin crews.
Traffic at the main international airports in Rome and Milan was normal as of Monday afternoon, airport officials said, despite warnings it may have to cease operations because of lack of fuel.
The new Alitalia will employ about 12,500 people including 1,500 pilots, 3,300 cabin staff and 7,650 technicians, workers and managerial staff, the Ansa news agency said.
"It's a first, important step," said Raffaele Bonanni of the CISL union.
But Massimo Notaro, the head of one of Italy's two main pilot unions, UP, described Sunday's deal as "completely unacceptable".
Five unions - SDL, ANPAC, UP, ANPAV and Avia - rejected the deal as "useless and provocative", while the four signatories - CGIL, CISL, UIL and UGL - were talking to the would-be buyers.
Last-ditch talks had been taking place overnight in Rome on a rescue package for Alitalia, which is operating under a bankruptcy commissioner.
Alitalia faces liquidation if a deal is not reached. The airline says it is running out of money to buy aviation fuel.
Under the rescue proposal the Italian consortium has put forward a 1bn euro ($1.4bn; £800m) offer for the airline.
Alitalia would merge with Air One, the country's second largest airline, and its 1.2bn euro debt would be absorbed by a second firm, which would then be liquidated.
Prime Minister Silvio Berlusconi has pledged to do all he can to save Alitalia. The government owns 49.9% in Alitalia.
In April, plans for the airline to be bought by Air France-KLM collapsed.
Meanwhile Sir Richard Branson, who owns half of airline Virgin Atlantic said Alitalia should go bankrupt.
"Unless the [Italian] government keeps pouring bad money after bad money, it's likely to disappear," he said.