The strikes by air traffic controllers and Alitalia cabin crew caused travel chaos which also affected other airlines, threatening to frustrate fans of soccer club AC Milan planning to travel to Wednesday's Champions League final in Athens.
The stoppages came as the Italian state sent a letter to its three shortlisted bidders for Alitalia, including a U.S. private equity group that is also gunning for Spain's Iberia.
It told them it wanted binding, cash offers for Alitalia by July 2. The Italian government said the bidder for a 39.9 percent stake could, if it wanted, buy the remaining 10 percent of the state's stake as well.
The idea could appeal to buyers looking to keep Alitalia free from political meddling, but unions said Italy should reconsider completely exiting the flag carrier.
''It would be better if the Treasury guarantees its presence in Alitalia,'' said Raffaele Bonanni, the leader of Italy's second largest trade union confederation, CISL.
Shares in Alitalia were 0.3 percent higher at 0.88 euros per share in early afternoon trade, slightly outperforming Milan's main index, which inched up 0.1 percent.
Alitalia, Europe's fifth-largest airline, is losing over 1 million euros ($1.4 million) a day as strikes and high fuel costs weigh. It has not posted an operating profit since 1998, despite several restructuring efforts.
The Italian state has told bidders their turnaround plans for Alitalia were more important than the offer prices, and let employees know the government is ready to help ease the pain from any job cuts.
ANGRY SOCCER FANS The bidders include Russia's Aeroflot and Alitalia's closest domestic rival, Air One. The third bidding consortium includes Texas Pacific Group, which is also bidding for Iberia.
Whoever buys Alitalia will inherit its notoriously strike-prone unions, who have already forced the airline to cancel hundreds of flights this month.
On Tuesday, a protest by cabin crews coincided with a air traffic controllers' strike in campaigns seeking better pay and conditions. Nearly 400 Alitalia flights were cancelled, or about half of the carrier's daily traffic.
The strikes threatened to affect up to 7,000 soccer fans planning to travel to Athens for Wednesday's Champions League final against Liverpool. Air traffic authorities warned of a risk to public security.
''Not allowing these people to fly is a serious problem,'' said Vito Riggio, head of Italy's civil aviation authority.
Meanwhile, the air traffic controllers strike promised to create travel headaches to other travellers as well.
German airline Deutsche Lufthansa expected major disruption to its Italian flights on Tuesday, cancelling 42 return flights.
Almost 5,000 passengers are set to be affected.
German budget carrier Air Berlin also expected to have to cancel some flights.
Some stranded travellers had less-than-noble gripes, including one man from Naples who complained his cancelled Brussels flight could expose his affair with another woman.
''My girlfriend thinks I am still in Belgium but I have come back to Italy because I have a lover here. She is expecting to meet me tonight,'' said the traveller, who asked not to be named.
''I don't know what I am going to do. This is what happens when you tell lies.'' REUTERS PBB DB2020