However, the agreement would still amount to the loss of about 3,000 jobs across the airline and was rejected by five smaller unions representing the airline's cabin crews and pilots.
Raffaele Bonnani, the secretary-general of the CISL union, one of the four signatories, said that the draft deal was as a "major first step to save Alitalia".
The five smaller unions, SDL, ANPAC, UP, ANPAV and Avia, who had not been party to the talks, condemned the deal as "useless and provocative" and said it did not "represent Alitalia's work force".
On Saturday, union sources had quoted Augusto Fantozzi, Alitalia's special administrator, as saying that as many as 12 aircraft could be grounded by Monday, and that with no agreement with the nine Alitalia unions to save the airline from bankruptcy, he would be obliged to start dismissal procedures.
"Up to tomorrow [Sunday] we have guaranteed flights, but not on Monday because no-one will supply us with kerosene," Fantozzi was quoted as saying.
In a later statement, Fantozzi denied that he had been alarmist, but acknowledged that "there are risks of supply difficulties which could threaten certain flights".
He said that the crews of 34 aircraft, which were currently not being used by the company, could be laid off from Monday, but said that he would only sack the entire workforce "when there is nothing else left to do".
Fantozzi, appointed last month when the airline asked to be declared insolvent, had warned unions on Wednesday that if a deal on restructuring was not reached before Friday, Alitalia would be made bankrupt quickly and he would start dismissing staff.
Alitalia, a national symbol for many Italians since it was founded in 1946, has lurched for years from crisis to crisis, and from restructuring plans to the latest takeover rescue scheme.
Its collapse would be a severe political blow to Silvio Berlusconi, Italy's prime minister, who had promised before the last elections that he would keep it flying under Italian control.
Berlusconi returned to Rome on Saturday from the south of the country to oversee the crisis, accusing the political left of being behind the "unreasonable behaviour" of the employees.
The Italian government owns 49.9 per cent of Alitalia, which has been surviving on a state loan of $425m made at the end of April.