DALLAS (CBSDFW.COM/AP) — Boeing has now made 96 flights to test a software update for its troubled 737 Max jet, according to the company’s CEO Dennis Muilenburg.

Muilenburg said Thursday, more test flights are planned in the coming weeks as Boeing attempts to convince regulators this type of plane is safe.

The Max was grounded by regulators around the world last month after deadly crashes involving the plane in Indonesia and Ethiopia.

A worker is pictured next to a Boeing 737 Max 9 airplane on the tarmac at the Boeing Renton Factory in Renton, Washington on March 12, 2019. (credit: Jason Redmond/AFP/Getty Images)

In both cases, faulty information from a sensor caused anti-stall automation to kick in when it wasn’t needed and push the plane’s nose down. Pilots struggled to counter the plane’s actions but were unable to avoid crashing.

Muilenburg, who spoke at a leadership forum in Dallas, said Boeing representatives have met with pilots and airline officials in the U.S., the United Kingdom, Singapore and China to discuss the changes it is making.

Separately, Democratic Sen. Edward Markey of Massachusetts introduced a bill in Congress Thursday requiring plane makers to provide airlines with all safety equipment now considered optional and to do so without an additional charge.

Markey said safety equipment that had not been installed on the Boeing 737 Max jets in Indonesia and Ethiopia might have saved them from fatal crashes. He says the equipment could have alerted crews to false readings from sensors implicated in those crashes.

Markey says plane makers shouldn’t treat safety features as luxuries that can generate additional fees like premium seats and extra bathrooms.

Boeing says its planes are equipped with “all critical features” necessary for safety. It has said it will provide two features missing in the two crashed planes free of charge.

Meantime, Southwest Airlines President Tom Nealon released a statement on the airline’s website Thursday saying flights on the 737 Max are suspended at least through August 5:

Our Teams are working to further increase the Reliability of our schedule and reduce the amount of last-minute flight changes—especially during the upcoming summer travel season. With that in mind, we’ve now modified our schedule through August 5, 2019 to add further stability for Customers booking their summer travel.

While the timing for the return to service of the MAX remains unclear, what is very clear is our commitment to operate a reliable schedule and provide the famous Customer Service you expect from us. Our revised summer schedule allows us to accomplish those objectives.

(© Copyright 2019 CBS Broadcasting Inc. All Rights Reserved. The Associated Press contributed to this report.)