CHICAGO — In his first major public address since the grounding of the 737 Max fleet, Boeing’s chief executive faced questions about the company’s credibility and its safety procedures following two fatal crashes involving the brand-new jet.

At the company’s annual meeting on Monday in Chicago, the chief executive, Dennis Muilenburg, sought to reassure shareholders, as the company faces increasing financial, legal and regulatory pressure. Shares of Boeing have lost about 10 percent of their value since the crash in March of an Ethiopian Airlines flight.

Mr. Muilenburg said Boeing was “making steady progress” in getting regulators to certify a fix for the anti-stall software that pushed the jet’s nose, a system that played a role in the Ethiopia crash and an earlier Lion Air accident in Indonesia.

[Update: Boeing believed a 737 Max warning light was standard. It wasn’t.]

“With the certified software update implemented, the 737 Max will be one of the safest airplanes ever to fly,” he said, according to his prepared remarks.