Boeing CEO Dennis Muilenburg told a congressional hearing Tuesday he was aware in early 2019, prior to the second deadly crash of the 737 Max last March, that a test pilot had raised questions about the safety of the jet. But Muilenburg said he was only told in the past few weeks of the details of the pilot's text messages and emails.

The messages, which date back to November 2016, were given to Department of Justice investigators in February, but were not released to the Federal Aviation Administration or other regulators until after the second 737 Max crash, months after their discovery. The messages also alluded to Boeing's possible efforts to hide safety concerns from the FAA other other regulators.

Senator Ted Cruz, a Republican of Texas, questioned why Boeing didn't flag the messages detailing the test pilot's concerns when Congress held meetings on the issue earlier this year.

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"I was involved in the document collection process, but I relied on my team to get the documents to the appropriate authorities," Muilenburg testified Tuesday. "I didn't get the details of the conversation until recently."

Tuesday was the one-year anniversary of the first of two crashes involving Boeing 737 Max jets that killed a total of 346 people. Testifying to the Senate Commerce Committee, Muilenburg was repeatedly questioned about what Boeing knew about the safety issues of the 737 Max and when it knew of them.

The CEO told Congress the aircraft company knows it made mistakes and is throwing everything into fixing the jet. Muilenburg apologized numerous times to family members for the crash and said he had called the FAA to explain that the company's disclosure to regulators should have been better.

"We have learned and are still learning from these accidents," Muilenburg said. "We know we made mistakes and got some things wrong. We own that, and we are fixing them."

Senator Tammy Duckworth, a Democrat from Illinois, said Boeing has not told the truth to Congress. "You knew back in 2016 that this was happening," Duckworth said.

Senators also criticized how the FAA regulates aircraft safety. "We are committed to participating in reform efforts," Muilenburg said.

About a dozen family members of those lost in the two 737 Max crashes were seated in the third row behind Muilenburg. Prior to the meeting, family members were warned against displaying pictures of those who had died in the crashes.

As Muilenburg walked into the hearing, Nadia Milleron, the mother of Samya Stumo, loudly demanded the right to hold up a picture of the crash victims. Capitol police said the family members would be ejected and arrested if they did not comply with the Senate's rules.

Boeing President and CEO Dennis Muilenburg on Capitol Hill in Washington, D.C., on Tuesday, October 29, 2019. AP

Standing before reporters shortly before the testimony, Muilenburg was much more reserved than in past statements about the Max crashes. He apologized to family members of the 346 people who died in the two crashes and said that he understood that the crashes happened on his watch.

Muilenburg said he didn't have knowledge of any plans by Boeing's board to force him to step aside when the problems with the 737 Max are fixed. But he said he was confident Boeing would be able to get the 737 Max, which has been grounded since mid-March, certified to fly again. Muilenburg has previously said it believes the planes could be ready to fly again by the end of the year.

"We have studied both crashes and we know what to fix," he said in a brief statement to reporters before addressing a Senate panel. "Once the Max returns to fly, it will be the safest airplane in the sky."

Roland Rehhorn and his wife Joan lost their 24-year-old daughter Angela in the Ethiopian Airlines crash. They told CBS News they didn't believe Muilenburg when he apologized. "If he's sorry, he would have resigned," Rehhorn said.

The couple brought their daughter's remains home from Africa just one week ago.

"It has torn me apart. Angela and I were so close," Rehhorn said.

Muilenburg will testify again on Wednesday before the House Transportation Committee.

The appearances in Washington, D.C., come as Boeing faces investigations by the Senate Commerce Committee and the House Transportation Committee as well as a criminal probe by the Justice Department. Boeing is also being sued by families of some of the 346 people who died in the crash of a Max off the coast of Indonesia on October 29, 2018, and another in Ethiopia on March 10, 2019.

In an exclusive interview with CBS News in May, Muilenburg apologized to the victims' families.

"I do personally apologize to the families, as I've mentioned earlier we feel terrible about these accidents, and we apologize for what happened, we are sorry for the loss of lives in both accidents," he said.

Kris Van Cleave contributed to this report.