Boeing Co. said Thursday it has completed a software update for its 737 Max jets, which have been grounded worldwide since March after they were involved in two fatal crashes.

The announcement is a sign of progress for the aircraft-maker’s efforts to get its best-selling jetliner back in the sky after a grounding that has already lasted more than two months.

The airplane manufacturer said it was providing additional information to address requests from the Federal Aviation Administration including details on how pilots interact with controls and displays in different flight scenarios.

Once the requests are addressed, Boeing will work with the FAA to schedule its certification test flight and submit final certification documentation, the company said.

The FAA is planning a meeting on May 23 in Fort Worth, Texas, with air regulators from around the world to update them on reviews of Boeing’s software fix and new pilot training.

The aviation regulator said Boeing had not yet submitted its final software package to the agency for approval.

Once that package is finalized, the FAA will schedule a flight test of the 737 Max’s new software by its pilots, the agency said.

The FAA sees an uncertain timeline for its review of the software update.

On Wednesday, acting FAA Administrator Dan Elwell said he expected Boeing to make its formal submission for its software update in the next week or so.

The 737 Max was grounded following a fatal Ethiopian Airlines crash that killed all 157 on board just five months after a similar crash of a Lion Air flight killed 189 people.

The company hopes the software upgrade and associated pilot training will add layers of protection to prevent erroneous data from triggering a system called MCAS, which activated in both crashes.

Boeing said it has completed associated simulator testing and its engineering test flight and developed training and education materials, which are now being reviewed by the FAA, global regulators and airline customers so that the jets can be returned to service.

To date, Boeing has flown the 737 Max with updated software, for more than 360 hours on 207 flights, the company said.

Boeing rose to session highs on the news. Since the March 10 crash of an Ethiopian Airlines jet, the shares slid 18 percent through Wednesday, the biggest decline on the Dow Jones Industrial Average.