Alitalia said in a statement that 315 flights were cancelled on Friday, with another 40 cancelled Thursday night and Saturday morning.
It was not immediately clear how many flights were cancelled at Air Italy. The strike was felt most in Sardinia, Air Italy's base, with about 30 flights cancelled.
Passengers were advised to check the status of their flight before going to the airport.
Alitalia passengers can do so on alitalia.com or by calling the airline's toll-free numbers: 800 65 0055 (from Italy) or +39 06 65649 (from overseas).
Photo: Alberto Pizzoli/AFP
The 24-hour strike, which involves pilots, flight attendants and ground personnel, was called by three unions to draw attention to what they called “the ongoing crisis at Alitalia and Air Italy”.
Money-losing Alitalia has been under special administration since 2017 when employees rejected a restructuring plan that would have laid off 1,700 workers out of an approximately 11,000.
The government has so far looked for buyers without success. A potential consortium of buyers for the ailing carrier fell apart last month after Atlantia, which operates Rome's airports, pulled out.
Unions plan to meet on Tuesday with Economy Minister Stefano Patuanelli.
What are my rights if a flight is cancelled?
If you're flying to, from or within the EU you have the right to either a refund or rebooking, and the airline must always offer you the choice.
If you're booked onto a later flight and have to wait for more than two hours, you're entitled to assistance such as food and drink. And in the case of cancellations at short notice you may also be able to claim compensation.
Find full details here.