"In order to focus on repairing this rostering problem this winter, Ryanair will eliminate all management distractions starting with its interest in Alitalia," it said in a statement.
"We have notified the Alitalia bankruptcy Commissioners that we will not be pursuing our interest in Alitalia or submitting any further offers for the airline."
- Italy's antitrust authority to investigate Ryanair over mass cancellations
- Italian lawyer sues airline after nine-hour flight next to fat man
- Italian court orders Ryanair to pay compensation over plane damage to family home
- The world's 'second worst' airport is in Italy
The Dublin-based carrier had announced a non-binding offer in July for Alitalia.
Alitalia, which has struggled to compete with low-cost rivals including Ryanair, went into administration at the start of May, moving the flagship airline a step closer to liquidation as efforts continue to find a buyer.
About 18 companies expressing an interest in a potential purchase had reportedly been given access to the company's figures, including also Delta Airlines, British Airways and Lufthansa.
Italy's government in May said it would provide a bridging loan to keep Alitalia planes flying for around six months.
Those interested in making binding offers have until October. If no buyer can be found, the administrators will have to organize Alitalia's winding-up.
Photo: poppet with a camera/Flickr