Muilenburg acknowledged errors in failing to give pilots more information on MCAS before the crashes, as well as for taking months to disclose that it had made optional an alarm that alerts pilots to a mismatch of flight data on the 737 MAX.
"We've made mistakes and we got some things wrong. We're improving and we're learning," he said.
The hearing, the highest-profile congressional scrutiny of commercial aviation safety in years, heaps pressure on a newly rejigged Boeing senior management team fighting to repair trust with airline customers and passengers shaken by an eight-month safety ban on its 737 MAX following the crashes, which killed 346 people.
Taking turns to grill Muilenburg during his first appearance at a hearing on Capitol Hill in the year since the first crash in Indonesia, senators suggested Boeing had not been completely honest and expressed dismay that the 2016 instant messages did not prompt an immediate reaction from the company.
"You have told this committee and you have told me half-truths over and over again," Senator Tammy Duckworth of Illinois, where Boeing is headquartered, said at one point.
Later in the hearing, Senator Jon Tester of Montana said: "I would walk before I would get on a 737 MAX ... You shouldn't be cutting corners."
For months, Boeing had largely failed to acknowledge blame, instead vowing to make a "safe plane safer." Tuesday's hearing represents Boeing's broadest acceptance of responsibility that it made mistakes, though Muilenburg and senior engineering executive John Hamilton stopped short of a game-changing display of contrition.
Boeing shares were up 0.6% at $343.03 on Tuesday afternoon.
U.S. Senator Roger Wicker, chairman of the Senate Commerce Committee, questioned Muilenburg over the company's delay in releasing internal messages. In those messages, a former test pilot described erratic behaviour of a simulator version of the same software now linked to the crashes, and also mentioned "Jedi-mind tricking" regulators over training requirements.
Wicker said those messages revealed a "disturbing level of casualness and flippancy."
Muilenburg said he apologised to the FAA administrator for the delay in turning over the messages, and said additional documents would likely be provided over time.
"We will cooperate fully," he added.
In his opening remarks, Muilenburg walked the committee through software upgrades to limit the authority of the stall-prevention system that has been linked to both crashes. He also listed changes at the company and its board of directors to improve safety oversight and transparency.
During one particularly tense exchange, Senator Maria Cantwell of Washington grilled Muilenburg and Hamilton over the extent of testing on the MCAS system. Cantwell asked Hamilton whether it was a mistake for Boeing not to test a failure mode similar to the scenarios faced by pilots in the crashes.
"In hindsight, senator, yes", Hamilton said. Both he and Muilenburg, however, pointed to extensive testing by engineers and pilots during the certification process that lasted years.
Muilenburg also acknowledged a "mistake on that implementation" for failing to tell the FAA for 13 months that it inadvertently made a so-called angle of attack disagree alert optional on the 737 MAX, instead of standard as on earlier 737s. The company insisted the missing display represented no safety risk.
"We got the implementation wrong," Muilenburg said, referring to the angle of attack disagree alert.
He added: "One of the things we've learned ... is we need to provide additional information on MCAS to pilots."
At one point, Senator Richard Blumenthal of Connecticut referred to the 737 MAX as "flying coffins."
Asked ahead of the hearing if he would resign, Muilenburg said that was "not where my focus is." He also declined to say if he or the board were considering his resignation after the plane returns to service.
Boeing on Tuesday ran full-page advertisements in major newspapers expressing condolences to the families and loved ones of those killed in the crashes.
"These two accidents occurred on my watch and I have a keen sense of responsibility," Muilenburg, who was stripped of his title as Boeing chairman by the board earlier this month, told reporters.
Family members, holding photos of victims of the crash, were seated just three rows behind Muilenburg during his testimony.
Wicker addressed the families, saying: "I promise to their loved ones that we will find out what went wrong and work to prevent future tragedies."
Indonesian investigators reported on Friday that Boeing, acting without adequate oversight from U.S. regulators, failed to grasp risks in the design of cockpit software on the 737 MAX, sowing the seeds for the Oct. 29, 2018, crash of Lion Air Flight 610.
On Tuesday, Muilenburg denied that Boeing's initial statements about the investigative findings from the Lion Air crash sought to shift blame onto pilots.
Muilenburg also rejected a characterisation of Boeing's "coziness with the FAA," though he said the certification process "can be improved."
Muilenburg was then asked why Boeing had not grounded the plane in the wake of Lion Air Crash. "If we could go back, we would make a different decision," he said.
(Reporting by David Shepardson in Washington; Writing and additional reporting by Eric M. Johnson in Seattle; Additional reporting by Tracy Rucinksi in Chicago and Tim Hepher in Paris; Editing by Bernadette Baum and Matthew Lewis)