The first occurred on October 29, 2018, when Lion Air Flight 610 crashed into the Java Sea 13 minutes after takeoff, killing all 189 passengers and crew.
The second took place on March 10, 2019 when Ethiopian Airlines Flight 302 crashed just six minutes after takeoff, with all 157 people aboard lost.
Investigators eventually blamed the accidents on the MAX's new automated manoeuvring characteristics augmentation system (MCAS), which forced both planes to nosedive.
Boeing is now overhauling the system by making it easier for pilots to override it and plans to return the aircraft to the skies.
Calhoun told CNBC that Muilenburg "has done everything right" following the twin tragedies.
"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," he told the news organisation.
Last month, relatives of those killed on both ill-fated flights arrived with photos of their lost loved ones at the beginning of a Senate Committee on Commerce, Science, and Transportation hearing in Washington, which discussed aviation safety and the future of Boeing's 737 MAX.
And last week, a group of members of Congress urged Muilenburg to resign or at least give up pay as a result of the crashes following two days of intense hearings.
Calhoun said Muilenburg would refuse his 2019 bonus and would not accept any stock awards until all MAX jets returned to the air, which could take a year or more.
He told CNBC the company still had confidence in Muilenburg – even though he lost his title of chairman last month.
"No one was hiding anything. It was a set of engineering decisions that ended up being wrong," he said.
"And our job now is to make sure that whatever processes we had, whatever process our regulator has, that those processes never allow for this to ever happen again."
Meanwhile, the crisis has stripped at least US$9 billion off the company's value, according to Bloomberg, and the firm is likely to suffer for years to come.
But the publication predicted the struggling CEO would still take home a salary, which was US$1.7m in 2018.
He also received several other perks, including access to company aircraft and life insurance premiums.
