The pilots of both aircraft lost control to an anti-stall system, known as MCAS, after it deployed in response to a faulty sensor. A total of 346 passengers and crew died in the two fatal accidents.
Mr Muilenburg faced the House Committee on Transportation and Infrastructure.
In a heated exchange, Steve Cohen, a Democrat congressman from Tennessee, asked the Boeing boss: “You say you’re accountable. What does accountability mean?
“Are you taking a cut in pay, are you working for free from now on so you can cure this problem?”
Gesturing to the families of the victims of the crashes who were at the hearing, he said: “These people’s relatives are not coming back. They’re gone. Your salary’s still on.
“Is anybody at Boeing taking a cut or working for free to try to rectify this problem? Like the Japanese would do?”
Mr Muilenburg said: “Congressman, it’s not about the money for me.”
Mr Cohen again asked: “Are you giving up any money?”
The response was: “Congressman, my board will conduct a comprehensive review.”
At that point, Mr Cohen said: “So you’re saying you’re not giving up any compensation at all?
“You’re continuing to work and make $30 million a year after this horrific two accidents that caused all these people’s relatives to go, to disappear, to die?”
Mr Muilenburg said: “Congressman, again, our board will make those determinations.”
In 2018, the Boeing leader was paid $23.4m but also cashed in share bonuses from previous years to bring his total income for the year to $30 million.
Earlier, another Democrat representative, Albio Sires from New Jersey, read out an email from a Boeing 737 worker sent to a senior executive expressing concern about the pressure staff felt under.
“For the first time in my history with Boeing I would be hesitant about putting my family on a Boeing airplane,” he wrote.
The Boeing 737 Max was grounded worldwide after the second crash in March 2019. Boeing expects it to fly again by the end of the year.