The consortium's earlier withdrawal had been an embarrassment for Silvio Berlusconi, Italy's prime minister, who last month promised a "miracle" to save Alitalia from bankruptcy.
The carrier's four largest unions had gathered to hold talks at Berlusconi's office on Thursday morning, hours before Alitalia's bankruptcy commissioner must present a rescue plan to aviation authorities or have its operating licence revoked.
Guglielmo Epifani, the head of CGIL, Italy's largest union which had previously rejected the deal, said: "An absolutely positive comprehensive agreement was reached."
Hopes that the pilot and flight staff unions could also be persuaded to change their mind rose after they held talks with a top aide of Berlusconi, late on Wednesday.
|Alitalia is haemorrhaging about $4.5m a day [AFP]
Antonio Divietri, the head of the Avia flight assistants union, said four of the unions representing pilots and flight staff would convene a meeting of their members to discuss the offer later on Thursday.
Divietri said indications that an industrial partner was set to enter the equation had "changed the situation", in an indirect reference to reports that Air France-KLM was in talks to join the CAI consortium with as much as a 25 per cent stake.
Air France-KLM is expected to hold a board meeting on Thursday which will discuss the developments at Alitalia.
The French-Dutch carrier has said in the past that it is willing to take a minority stake in Alitalia if it can return to profit.
Industry sources said Francesco Mengozzi, a consultant for Air France-KLM, had sent a "message of interest" from Jean-Cyril Spinetta, the company's chairman, to the Italian government.
Air France-KLM dropped a takeover bid for Alitalia in April in the face of union resistance.
Alitalia, which employs nearly 20,000 people, faces a Thursday deadline to come up with a solid rescue plan or lose its licence to fly.
The company, which is 49.9 per cent state owned, is haemorrhaging about $4.5m a day with a debt of about $1.7bn.
Augusto Fantozzi, the airline's special administrator, is due to present a plan to Enac, Italy's civil aviation authority, on Thursday that calls for a reduction in the number of flights.
Alitalia has been surviving on a loan of $450m made in late April from public funds after the takeover talks with Air France-KLM collapsed.
The European Commission is investigating whether the loan meets EU bailout rules after expressing grave doubts.