Boeing's new chairman gave Dennis Muilenburg a vote of confidence on Tuesday and said the embattled CEO has offered to forgo all bonuses this year as the company grapples with the fallout of two crashes of the 737 Max.

Lawmakers on Capitol Hill last week railed against Muilenburg over his compensation of $23.4 million, including a $13.1 million incentive bonus, in 2018, despite the crash of a 737 Max in Indonesia in October 2018. Another 737 Max crashed in Ethiopia five months later. Boeing doesn't plan to claw back 2018 compensation from Muilenburg.

A flight-control system known as MCAS that Boeing included on the jets has been implicated in both crashes, which killed all 346 people on the flights. At last week's two hearings, lawmakers slammed the manufacturer for failing to put in more safeguards and shared documents showing Boeing employees had safety concerns about the planes.

"From the vantage point of our board, Dennis has done everything right," Chairman Dave Calhoun told CNBC. "Remember, Dennis didn't create this problem. From the beginning, he knew that MCAS could and should have been done better and he has led a program to rewrite MCAS to alleviate all of those conditions that ultimately beset two unfortunate crews and the families and victims."

Calhoun also said in the "Squawk Box" interview that Muilenburg called him Saturday morning "with the purpose of suggesting that he not take any compensation for 2019 in the form of bonuses, which of course is most of your compensation."

"It came in two fronts: one, no short-, no long-term bonus, and three, no consideration for equity grants, until the Max in its entirety is back in the air and flying safely," Calhoun said, adding that it could take until 2021.

A Boeing spokesman told CNBC last week that there is "no path to the annual incentive plan" this year.

Last week's two days of hearings were tough for Muilenburg, Calhoun said. The night after the first hearing, Muilenburg listened to the victims' families.

"He listened for several hours to every story, every story the victims' families presented to him. Changed him for life," Calhoun said.

Boeing's board stripped Muilenburg of his chairmanship on Oct. 11 saying it had "full confidence" in him as CEO and that the move would help him better address the 737 Max issues. Regulators grounded the planes worldwide after the second crash in March, forcing Boeing to halt deliveries and slash production of its best-selling aircraft.

Boeing has been scrambling to get software fixes for the planes approved by regulators but so far they haven't signed off. The manufacturer plans to continue using the 737 Max brand name, Calhoun said.

Some of Boeing's 737 Max customers, including Southwest and American, have complained about hundreds of millions of dollars in lost revenue because of the Max grounding. Calhoun reiterated that the manufacturer plans to have settlements with its customers and said its balance sheet can handle that.

Boeing took a nearly $5 billion after-tax charge in the second quarter to compensate airlines.

Muilenburg said on the company's second quarter earnings call in July that Boeing could halt production altogether, but Calhoun on Wednesday said Boeing has no plans to reduce the already lowered 737 Max production rate of 42 a month. 

Boeing's stock was up 1.2% in morning trading, and about 10% so far this year, roughly half the percentage gain of the broader market.

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