Dennis Muilenburg, Boeing’s chief executive, said he considered stepping down after the company’s signature 737 Max had two fatal accidents.

“It’s fair to say I’ve thought about it,” he said at the DealBook conference last week, during a wide-ranging discussion of how he has handled the fallout from the crashes, which killed 346 people.

Mr. Muilenburg said he decided to remain in his position because he felt responsible for getting the company through the crisis. “I don’t see running away from a challenge, resigning, as a solution,” Mr. Muilenburg said. “These two accidents, they happened on my watch on Boeing. And I feel obligated, I feel responsible to stay on it.”

Mr. Muilenburg said he decided to give up “tens of millions of dollars” in incentive pay after meeting recently with families of victims of the crashes. “I felt it was important for me to forgo those bonuses and send a message of responsibility,” he said.