CHICAGO (CBS/AP) — Seeking to reassure travelers, United Airlines CEO Oscar Munoz has promised to board his company’s first Boeing 737 Max jet to take flight once regulators clear the aircraft to fly again.

Munoz made the promise after Chicago-based United’s annual shareholders meeting on Wednesday. He said the company also will take steps to educate customers and employees about why United feels it’s safe to resume flights of the 737 Max.

Chicago-based Boeing has said it completed its software fix for the anti-stall system implicated in two deadly crashes in October and March, which killed a total of 346 people. However, the company has not yet submitted final paperwork to regulators or scheduled a mandatory test flight with Federal Aviation Administration experts.

Representatives from the FAA will meet with officials from 33 other global aviation regulators on Thursday to discuss the steps the FAA already has taken, and what must still be done before 737 Max planes fly again.

Acting FAA Administrator Daniel Elwell repeated that his agency won’t lift the grounding of the Max until it is safe. He said people eventually will get back on the plane.

“Is public confidence shaken right now? Maybe,” Elwell told reporters, adding that once the FAA finishes its study of Boeing’s changes to the plane, “the public will fly it and the public will be confident in U.S. and global travel.”

Three U.S. airlines — Southwest, American and United — have 72 Max jets and hoped that with the software fix and additional training for pilots, they could be flying again by August.

Elwell declined to say whether that would happen.

“If it takes a year to find everything we need to give us the confidence to lift the (grounding) order, then so be it,” Elwell said. “I’m not tied to a timetable.”

Because the plane was designed and built in the United States, the FAA is almost certain to be the first to certify it safe to fly. Regulators from China, Europe and Canada have indicated they plan their own reviews before ungrounding the plane, but FAA officials hope they don’t wait too long.

At Thursday’s meeting, FAA will share its safety analysis of the Max.

FAA officials hope foreign regulators will indicate “what else they would like to see from us so that we can help them with their decisions to unground,” said Ali Bahrami, FAA’s associate administrator for aviation safety.

Meantime, China has continued to pressure Boeing, with three state-owned airlines demanding to be reimbursed for losses after the 737 Max fleet was grounded.

(© Copyright 2019 CBS Broadcasting Inc. All Rights Reserved. The Associated Press contributed to this report.)