In an exclusive interview with CBS News, Boeing CEO Dennis Muilenburg apologized to families involved in the two crashes that killed 346 people and led to the grounding of all 737 Max jets.

"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," Muilenburg told Norah O'Donnell, the incoming managing editor and anchor of the "CBS Evening News."

"We are sorry for the impact to the families and the loved ones that are behind, and that will never change, that will always be with us. I can tell you it affects me directly as a leader of this company, it's very difficult."

In October 2018, Lion Air Flight 610 crashed 12 minutes after takeoff, killing all 189 people on board. In March of this year, Ethiopian Airlines Flight 302 crashed into the ground six minutes after takeoff, killing 157 people. In response, all Boeing 737 Max planes were grounded worldwide.

The company has said a flight-control software update is ready and awaiting Federal Aviation Administration (FAA) certification.

"We can't change what has happened in these accidents but we can be absolutely resolute in what we're going to do on safety going forward," Muilenburg said. "So I am sorry for that, we apologize to the families that have been affected, we apologize more broadly to the traveling public where confidence has been affected."

"People who were scared about flying?" O'Donnell asked.

"We've impacted our airline customers, right, we regret that as well, and we're stepping up. We're taking responsibility. We know we have improvements we can make. We will make those improvements and we're committed to safety for the long run," Muilenburg said.

Watch more of O'Donnell's interview with Muilenburg Thursday, May 30, 2019 on "CBS This Morning," 7 a.m. ET.