In an appearance that began at 10 a.m.
EDT (1400 GMT) before the Senate Commerce Committee, Muilenburg acknowledged errors.
"We've made mistakes and we got some things wrong.
We're improving and we're learning," he said.
For months, Boeing had largely not acknowledged blame and, instead, vowed to make a "safe plane safer." Tuesday's hearing represents Boeing's broadest acceptance of responsibility that it made mistakes.
Senator Roger Wicker, the committee chairman, questioned Muilenburg over the company's delay in releasing internal messages, first published by Reuters.
In those messages, a former test pilot described erratic behavior of a simulator version of the same software now linked to the deadly 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 apologized 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," Muilenburg added.