The CEO's $23.4 million in bonus compensations previous year recently came under fire from Capitol Hill.
Muilenburg is now under investigation by the Justice Department and Congress.
Muilenburg admitted that fixing the MCAS is taking longer than expected.
"Dennis didn't create this problem, but from the beginning he knew that MCAS should and could be 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", Mr Calhoun said on CNBC.
Last week, lawmakers grilled Muilenburg about his $23.4 million compensation, including a $13.1 million incentive bonus in 2018.
The former General Electric Co. vice-chairman, who has expertise in aerospace manufacturing and corporate turnarounds, was named chairman when Muilenburg was stripped of the role on october 11.
The chairman of the U.S. House Transportation and Infrastructure Committee and the head of its aviation subcommittee said on Monday that it will continue its investigation into two fatal 737 MAX crashes after Boeing's testimony prompted new questions. Muilenburg will receive no stock grants until the plane is fully back in service. He said that process, which includes deliveries of about 400 planes that Boeing has built during the grounding but not yet delivered, won't be completed until early 2021.
Boeing completes abort test on new human spaceflight capsule
Since the, the United States has relied on purchasing seats on Russian Soyuz capsules to reach the International Space Station. These systems are created to protect astronauts in the event that an emergency happens before liftoff once launch day arrives.
Calhoun said the crashes also revealed "flawed" assumptions about how pilots would react to a malfunction of the system. "He is an asset".
'Mr. Muilenburg's answers to our questions were consistent with a culture of concealment and opaqueness and reflected the enormous pressure exerted on Boeing employees during the development and production of the 737 Max, ' said Peter DeFazio, D-Ore., chairman of the House Transportation Committee and Rick Larsen, D-Wash., chairman of the aviation subcommittee. The call was made "with the objective of suggesting that he not take any compensation for 2019 in the form of bonuses, which of course is most of your compensation [as a chief executive]", Calhoun told the network. "As recently as Sunday evening, he has our confidence".
Boeing just replaced Kevin McAllister, who had been president and CEO of Boeing Commercial Airplanes, the unit of Boeing that builds the Max and other passenger jets.
A Boeing employee for 30 years, Muilenburg assumed the role of CEO in 2015.
Calhoun said that Muilenburg met with families of crash victims last week when he was in Washington for the two days of hearing, an experience that "changed him for life", according to Calhoun.