New York (CNN Business) Boeing's CEO on Monday said the safety systems on its 737 Max jets were properly designed, but he added that the airline is working to make them safer following two recent deadly crashes.

Dennis Muilenburg said the pilots did not "completely" follow the procedures that Boeing had outlined to prevent the kind of malfunction that probably caused a March 10 crash of an Ethiopian Airlines jet. A Lion Air 737 Max crashed under similar circumstances in October.

The company's anti-stall software, called MCAS, was a common link in both crashes. It met Boeing's design and safety criteria, and adhered to certification protocols, Muilenburg told reporters following Boeing's annual shareholder meeting in Chicago.

"When we design these systems, understand that these airplanes are flown in the hands of pilots," he said. He added that Boeing was unable to find any "technical slip or gap" in building its MCAS software.

Ethiopian officials said earlier this month that pilots flying Ethiopian Airlines Flight 302 repeatedly performed all of Boeing's procedures , but could not control the plane before it crashed.

Boeing has accepted its role in the crashes.

"It's our responsibility to eliminate this risk. We own it and we know how to do it," Muilenburg said on April 4

On Monday, Muilenburg reiterated that Boeing can make some improvements to make the 737 Max safer to fly.

"Going forward we have identified a way to improve," he said. "I am confident that that again will make one of the safest airplanes in the air to fly. ...We know this is a link in both accidents that we can break."

Facing off with shareholders

Boeing executives faced shareholders' tough questions about the 737 Max crisis at the meeting.

Shareholders had a lot to gripe about. The company's stock has lost about 10% of its value since the March 10 crash , which prompted a worldwide grounding of the 737 Max last month.

Boeing last week announced earnings fell 21% in the first quarter because of the crisis. Boeing suspended its share repurchase plans to conserve cash.

Muilenburg started his remarks Monday with a moment of silence for the 346 people killed in the two crashes, according to his prepared remarks reviewed by CNN Business. He insisted that Boeing makes safety its top priority, and he said the company has been doing everything it can to find a solution. And he vowed the 737 Max will become the safest plane in the air once Boeing develops a fix to the automatic safety feature that is the focus of the two crash investigations.

"These enduring values are at the core of everything we do," Muilenburg said in his prepared remarks. "Yet, we know we can always be better. We have a responsibility to design, build and support the safest airplanes in the sky. The recent accidents have only intensified our dedication to it."

Shareholders voted on one proposal that would have separated the positions of chairman and CEO , both of which are now held by Muilenburg. A preliminary vote on that measure was supported by only 34% of the shares — better than the amount of support a similar measure received last year, but still far short of a majority.

The resolution predated the current 737 Max crisis. Two shareholder advisory firms recommended votes in favor of the resolution this time.

"Shareholders would benefit from the most robust form of independent oversight to ensure that the company's management is able to regain the confidence of regulators, customers and other key stakeholders," said one of those services, ISS, in a note urging support for the measure.

Muilenburg also said a preliminary vote showed that 92% of the shares supported the company's executive compensation package.

A small group of protesters braved pouring rain and cold outside the annual meeting. Most held large photos of some of the people killed on the two flights. One held signs reading "Boeing's arrogance kills," and "Prosecute Boeing & execs for manslaughter."

Boeing BA Questions remain as to whetherdid everything it could to ensure the planes were as safe as possible. For example, four Boeing employees called an Federal Aviation Administration whistleblower hotline to report damage to the wiring of sensors, CNN has reported. And Boeing made airlines pay extra if they wanted an alert that lets pilots know if two sensors are contradicting each other. After the crashes, the company said in congressional testimony it would make that feature standard on planes in the future.

Muilenburg defended that earlier decision to include the alert as an option in his prepared remarks.

"We don't make safety features optional," he said. "Every one of our airplanes includes all of the safety features necessary for safe flight."

Muilenburg said again that the company is getting close to a software fix. It has completed 146 flights of the 737 Max, totaling roughly 246 hours of air time with the updated software. He said he personally has flown on two of those test flights.

And in response to a shareholder's question, Muilenburg said Boeing executives would be on some of the early commercial flights once the planes return to service.

"It will include me and many others," he said. "This is a really important part in showing our confidence in our product. Our Boeing employees are very supportive of doing that."

Muilenburg faced several questions from shareholders about how the problem with the 737 Max was able to happen.

"You seem to have rushed the 737 [Max] into production and lost sight of some basic fail-safe things that go on," said one shareholder. "It never should have happened that you had one easily damaged sensor control a new, critically designed safety feature."

Muilenburg insisted that the 737 Max was not rushed. He said the plane took six years to develop and that the equipment had been deemed safe.

"I want to assure you safety is our top priority," Muilenburg said. "That said, we can always improve."

The safety feature forces down the plane's nose if a sensor detects it is climbing too fast and at risk of a stall. Apparently the sensor on the two flights gave a false reading. Two weeks after the Ethiopian crash, Boeing announced the software fix would add data from a second sensor that measures the horizontal tilt of the plane.

-- CNN's Patricia DiCarlo and Glen Dacy contributed to this report.