DENVER (REUTERS) - Boeing Co made mistakes that need to be addressed, Southwest Airlines Co Chief Executive Officer Gary Kelly told shareholders on Wednesday (May 15), but he added he is still hopeful the grounded 737 MAX jets will return to service this summer.

Southwest, the world's largest MAX operator, has cancelled 160 daily flights through Aug 5 as its 34 MAX jets remain parked at a facility in a California desert, hitting revenue and costs and forcing the airline to put growth plans on hold.

"All of our growth is with the MAX," Kelly said in response to a shareholder question at the company's annual general meeting.

The MAX jets represent less than 5 per cent of the low-cost carrier's fleet of about 750, but the airline has at least 249 more on order.

Boeing is under pressure to deliver a software fix and new training to convince global regulators that the narrowbody jetliner is safe to fly following two fatal crashes, one on Lion Air in Indonesia last October and another on Ethiopian Airlines in March.

The Boeing 737 MAX plane was grounded worldwide in mid-March after the two crashes which killed a combined 346 people.

Federal Aviation Administration acting chief Dan Elwell told lawmakers on Wednesday he expects Boeing to submit a software fix soon, and said he was concerned by the planemaker's lengthy delay in disclosing a software anomaly.

Southwest shareholders rejected a motion to split Kelly's dual role as CEO and chairman of the board at the annual meeting.