WASHINGTON/CHICAGO (Reuters) - The Federal Aviation Administration met for three hours on Friday with representatives from the three major U.S. airlines that own now grounded Boeing 737 MAX jets and their pilots’ unions to discuss two fatal crashes and the path forward.

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More than 300 Boeing 737 MAXs have been grounded worldwide after a total of 346 people died in a Lion Air crash in Indonesia in October and in an Ethiopian Airlines crash outside Addis Ababa last month.

American Airlines Group Inc, United Airlines and Southwest Airlines Co officials attended the meeting, where FAA Acting Administrator Dan Elwell said he wanted to know operators’ and pilots’ thoughts before the agency decides to return the 737 MAX to service.

Elwell said the meeting participants’ “operational perspective is critical input as the agency welcomes scrutiny on how it can do better.”

American said in a statement it was “confident in the direction the FAA is heading” and would continue to work collaboratively in this process.

Pilots from American and Southwest, the two largest U.S. MAX operators, said they welcomed the meeting but noted that many issues still needed to be discussed and debated before the MAX flies again.

“We have to unground the confidence in this airplane,” Dennis Tajer, spokesman for the Allied Pilots Association which represents American’s pilots, told reporters outside FAA headquarters.

“We take off our watches and put the calendars in the drawer,” he added, suggesting that rebuilding confidence in the aircraft could take some time.

American and United have removed the 737 MAX from their schedules through early June, while Southwest on Thursday extended the removal of its 34 MAX jets through Aug. 5, leading to around 160 daily flight cancellations during the revised summer schedule.

Boeing is reprogramming software on the 737 MAX to prevent erroneous data from triggering an anti-stall system known as MCAS that is under mounting scrutiny following the two deadly nose-down crashes.

The FAA said the meeting covered a review of the preliminary findings of the two crash investigations and an overview of Boeing’s anticipated software enhancements and pilot training.

The plane’s certification and training have been questioned following a 2004 decision by Congress to allow manufacturers an expanded role in the FAA’s aircraft oversight.

Captain Jon Weaks, president of the Southwest Airlines Pilots Association, said in a letter he was concerned that this concept “may be too ingrained to reverse” and complicated by federal budget and personnel shortfalls, but called for continued scrutiny of Boeing.

The FAA has convened a joint review with aviation regulators from China, Europe, Canada, Brazil, Indonesia, Ethiopia and other countries.

Federal prosecutors, the Transportation Department inspector general’s office and a blue-ribbon panel are also reviewing the plane’s certification.

“The first and most important goal of all of the entire process should be to protect the lives of our passengers and the traveling public in general,” said Weaks.