The results prove the company "is on the right track," said Luigi Gubitosi, who was appointed by the government in May 2017 along with two others to steer the company then threatened with bankruptcy.
"We end the month of June with a growth of 10.6 percent in passenger numbers after a 7.6 percent growth in May," he told the Italian daily Corriere della Sera.
"Over the second quarter, earnings before interest, tax, depreciation and amortisation (EBITDA) will be balanced after a loss of 100 million last year."
The airline which employs more than 11,000 people has struggled to compete with low-cost European rivals.
It went into administration last May at the request of its shareholders after staff rejected job and salary cuts as part of a two-billion-euro ($2.4 billion) rescue plan.
It has been the subject of three offers, from German airline giant Lufthansa, another from US private equity group Cerberus, and a joint EasyJet-Air France bid.
The deadline for the sale, initially set for April, was postponed until late October by Rome.