CHICAGO — The CEO of Boeing defended the company's safety record and declined to take any more than partial blame for two deadly crashes of its best-selling plane even while saying Monday that the company has nearly finished an update that "will make the airplane even safer."

Chief executive officer Dennis Muilenburg took questions from the media for the first time since accidents involving the Boeing 737 Max in Indonesia and Ethiopia killed 346 people and plunged Boeing into its deepest crisis in years.

Muilenburg said that Boeing followed the same design and certification process it has always used to build safe planes, and he denied that the Max was rushed to market.

"As in most accidents, there are a chain of events that occurred," he said, referring to the Lion Air crash on Oct. 29 and the March 10 crash of an Ethiopian Airlines Max. "It's not correct to attribute that to any single item."

The press conference, held after Boeing's annual meeting in Chicago, came as new questions have arisen around the Max, which has been grounded worldwide since mid-March.

Southwest Airlines said over the weekend that Boeing did not disclose that a safety feature on the 737 — an indicator to warn pilots about the kind of sensor failure that has been linked to both accidents — was turned off on the Max. Southwest said it found out only after the first crash of the Lion Air Max.

Boeing, in a statement Monday, said the indicator was not necessary for safe operation of the Max and was part of an optional feature available to airlines. Boeing said it will include the indicator on all future Max deliveries and will tell airlines that have already taken deliveries of the plane how to enable the feature.

Published reports said that federal regulators and congressional investigators are examining safety allegations relating to the Max that were raised by about a dozen purported whistleblowers.

And the pilots' union at American Airlines said Boeing's proposal for additional pilot training on the Max doesn't go far enough. For instance, the union for American Airlines pilots wants, at a minimum, mandatory additional training to include video demonstrations of how to respond to failures of systems on the plane.

The annual meeting came six months to the day since the Lion Air crash. Muilenburg told shareholders that Boeing is close to completing an upgrade to flight software on the Max "that will ensure accidents like these never happen again."

In the brief news conference that followed, Muilenburg said — as he has several times before — that the accidents resulted from a "chain of events" that included the erroneous activation of flight software known as MCAS.

Boeing has conceded that in both accidents, MCAS was triggered by faulty readings from a single sensor and pushed the planes' noses down.

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"We know this is a link in both accidents that we can break. That's a software update that we know how to do ... this will make the airplane even safer," Muilenburg said.

Muilenburg took six questions from reporters, including whether he will resign — he has no intention of doing that — and left as reporters persisted, including one who pointed to the deaths of 346 people and urged the CEO to take more questions.

Besides the software update, Boeing will present the Federal Aviation Administration with a plan for training pilots on changes to MCAS. The company is pushing for training that can be done on tablet computers and, if airlines want to offer it, additional time in flight simulators when pilots are due for periodic retraining.

A requirement for training in simulators would further delay the return of the Max because of a relatively small number of flight simulators.

The union for American Airlines pilots wants mandatory additional training on checklists for responding to certain emergencies.

"Not every pilot that goes out there and flies is a Boeing test pilot," said Dennis Tajer, a 737 pilot and spokesman for the pilots' union at American. "The responsibility to train those men and women doesn't rest just with the airlines, it rests with Boeing and the FAA, too. If something happens anywhere in the world, it affects all of us."

Boeing is one of the Charleston region's top employers, with about 7,000 worker and contractors. The company builds its wide-body 787 Dreamliner commercial plane in North Charleston and has other facilities that design and build engine parts and make interior parts for the Dreamliner.